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全部话题 - 话题: sins
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l**********t
发帖数: 5754
1
Chapter 2.4 The Divine Way of Deliverance
God clearly intends that this consideration should lead to our practical
deliverance from sin. Paul makes this quite plain when he opens chapter 6 of
his letter with the question: “Shall we continue in sin?” His whole being
recoils at the very suggestion. “God forbid!”, he exclaims. How could a
holy God be satisfied to have unholy, sin-fettered children? And so “how
shall we any longer live therein?” (Romans 6:1, 2). God has surely
therefore made adequat... 阅读全帖
l**********t
发帖数: 5754
2
chapter 8.2 Faith Is Again The Key
As for forgiveness, so equally for the coming upon us of the Holy Spirit,
the whole question is one of faith. As soon as we see the Lord Jesus on the
Cross, we know our sins are forgiven; and as soon as we see the Lord Jesus
on the Throne, we know the Holy Spirit has been poured out upon us. The
basis upon which we receive the enduement of the Holy Spirit is not our
praying and fasting and waiting, but the exaltation of Christ. Those who
emphasize tarrying and ... 阅读全帖
l**********t
发帖数: 5754
3
Chapter 2.4 The Divine Way of Deliverance
God clearly intends that this consideration should lead to our practical
deliverance from sin. Paul makes this quite plain when he opens chapter 6 of
his letter with the question: “Shall we continue in sin?” His whole being
recoils at the very suggestion. “God forbid!”, he exclaims. How could a
holy God be satisfied to have unholy, sin-fettered children? And so “how
shall we any longer live therein?” (Romans 6:1, 2). God has surely
therefore made adequat... 阅读全帖
l**********t
发帖数: 5754
4
chapter 8.2 Faith Is Again The Key
As for forgiveness, so equally for the coming upon us of the Holy Spirit,
the whole question is one of faith. As soon as we see the Lord Jesus on the
Cross, we know our sins are forgiven; and as soon as we see the Lord Jesus
on the Throne, we know the Holy Spirit has been poured out upon us. The
basis upon which we receive the enduement of the Holy Spirit is not our
praying and fasting and waiting, but the exaltation of Christ. Those who
emphasize tarrying and ... 阅读全帖
R*o
发帖数: 3781
5
来自主题: TrustInJesus版 - Study and Exposition of Romans 1:18-32
G. Contribution of the Passage to Systematic Theology
This passage contributes in numerous ways to systematic theology. First, our
understanding of bibliology or more specifically, revelation (i.e., the stu
dy of how God makes himself known) is greatly enhanced by this passage. Here
in Romans 1:18-20 Paul does not appeal to inscripturated truth per se (i.e.
, truth revealed in the pages of the OT), but rather to the continual revela
tion of God in and through creation and in his wrath against si... 阅读全帖
R*o
发帖数: 3781
6
来自主题: TrustInJesus版 - Study and Exposition of Romans 1:18-32
G. Contribution of the Passage to Systematic Theology
This passage contributes in numerous ways to systematic theology. First, our
understanding of bibliology or more specifically, revelation (i.e., the stu
dy of how God makes himself known) is greatly enhanced by this passage. Here
in Romans 1:18-20 Paul does not appeal to inscripturated truth per se (i.e.
, truth revealed in the pages of the OT), but rather to the continual revela
tion of God in and through creation and in his wrath against si... 阅读全帖
R*o
发帖数: 3781
7
来自主题: TrustInJesus版 - Study and Exposition of Romans 2:1-16
2:1-4 The Jew who judges Gentiles has no excuse because at the same point at
which he judges another he condemns himself. Why? Well, when he judges, he
admits that such behavior is wrong, and worthy of just punishment from God,
yet he himself knowingly commits the same sins.
Paul’s point is that since God’s judgment is based on truth and not on any
fudging of the grades for the sake of the “chosen” crowd, the Jew is equa
lly held accountable to God. Jews cannot condemn others for their sins when... 阅读全帖
R*o
发帖数: 3781
8
来自主题: TrustInJesus版 - Study and Exposition of Romans 6:1-14
B. Translation of Passage in NET
6:1 What shall we say then? Are we to remain in sin so that grace may increa
se?
6:2 Absolutely not! How can we who died to sin still live in it?
6:3 Or do you not know that as many as were baptized into Christ were baptiz
ed into his death?
6:4 Therefore we have been buried with him through baptism into death, in or
der that just as Christ was raised from the dead through the glory of the Fa
ther, so we too may walk in new life.
6:5 For if we have become united ... 阅读全帖
R*o
发帖数: 3781
9
来自主题: TrustInJesus版 - Study and Exposition of Romans 6:1-14
B. Translation of Passage in NET
6:1 What shall we say then? Are we to remain in sin so that grace may increa
se?
6:2 Absolutely not! How can we who died to sin still live in it?
6:3 Or do you not know that as many as were baptized into Christ were baptiz
ed into his death?
6:4 Therefore we have been buried with him through baptism into death, in or
der that just as Christ was raised from the dead through the glory of the Fa
ther, so we too may walk in new life.
6:5 For if we have become united ... 阅读全帖
J*******g
发帖数: 8775
10
来自主题: TrustInJesus版 - 回家
你对这段经文理解有问题。
这段是说信耶稣应该是如重生一般,真正信主的人要认识自己的罪,而避免延续之前的
恶的行为。信主的人身上会看到行为向好的方向的变化。
但不排除基督徒犯错。请看,在你引的经文前两章:
1 John 1
8 If we claim to be without sin, we deceive ourselves and the truth is not
in us. 9 If we confess our sins, he is faithful and just and will forgive us
our sins and purify us from all unrighteousness. 10 If we claim we have not
sinned, we make him out to be a liar and his word is not in us.
1 John 5
16 If you see any brother or sister commit a sin that does not lead to death
, you shoul... 阅读全帖
J*******g
发帖数: 8775
11
来自主题: TrustInJesus版 - 与无神论少年讨论基督教
这是中译本的一个意译,目的是为了让读者更容易理解圣经。而英文版本没有这样翻译。
但是这个问题是很普遍的问题,google一下就可以看到解释。我这里把NET bible的解
释粘贴过来,希望您能了解的更深入。
God gave Moses a preview of all that would take place in his dealings with
Pharaoh (vv. 21-23). When God said He would harden Pharaoh’s heart (v. 21),
He was not saying that Pharaoh would be unable to choose whether he would
release the Israelites. God made Pharaoh’s heart progressively harder as
the king chose to disobey God’s will (cf. Lev. 26:23-24).
“The hardening of Pharaoh is ascribed to... 阅读全帖
n********n
发帖数: 8336
12
1.我们既因信称义,就借着我们的主耶稣基督,得与神相和。
Therefore, since we have been justified through faith, we have peace with
God through our Lord Jesus Christ,
2我们又借着他,因信得进入现在所站的这恩典中,并且欢欢喜喜盼望神的荣耀。
through whom we have gained access by faith into this grace in which we now
stand. And we rejoice in the hope of the glory of God.
3不但如此,就是在患难中,也是欢欢喜喜的。因为知道患难生忍耐。
Not only so, but we also rejoice in our sufferings, because we know that
suffering produces perseverance;
4忍耐生老练。老练生盼望。
perseverance, character; and character, ho... 阅读全帖
h*******r
发帖数: 1
13
来自主题: Computation版 - [转载] 求一个方程的解析解
【 以下文字转载自 Mathematics 讨论区 】
【 原文由 humorstar 所发表 】
a*sin(theta)*sin(theta)+b*sin(theta)*cos(theta)+c*cos(theta)*cos(theta)
+d*sin(theta)+e*cos(theta)+f = 0
a~f是常数,求theta,能求出解析解吗?
另外一个方程:
a*sin(theta)^4+b*sin(theta)^3+c*(sin(theta)^2)*cos(theta)+d*sin(theta)^2
+e*sin(theta)*cos(theta)+f*sin(theta)+g = 0
这个有可能有解析解吗?没有的话,用什么数值方法比较快?
谢谢.
G**B
发帖数: 371
14
来自主题: _BibleStudy版 - 【每日灵修】每天更新~
【今日默想禱讀經文】哥林多前書 1:8
他也必堅固你們到底、叫你們在我們主耶穌基督的日子、無可責備。
【今日信息】無可責備的人生 By Rev. Andrew Tsai
人有可能活出一個無可責備的人生嗎?
答案是有可能。但是在
約翰一書1:8不是說" 我們若說自己無罪、便是自欺、真理不在我們心裏了。"
我們每個人若都是罪人,我們如何能活出無可責備的人生呢?
我記得,當我正要步入青少年期時,有一次我父親把我叫來,送給我一張卡片,上面
有一顆很漂亮的樹,樹上結滿了果子。然後他就告訴我說:"我希望你的人生就像這棵
果樹一樣,能活出一個無悔的人生"
當時我覺得,這很容易阿,只要不做壞事,不就能達到了嗎?
但是當我愈長大,我就發現愈來愈難,因為我發現我自己裡面沒有良善,我發現立志
為善由得我,但是行出來由不得我,所以我非常痛苦,愈想要為善,就愈痛苦。
後來我遇到一位新派神學的牧師;(新派神學其實就是不信派,是惟理性派);他跟
我說,你為什麼要如此痛苦呢?你可以從這當中解脫阿,因為神是你自己想出來的,我
思故我在,只要你不要想,神就不存在了。
我恍如得著至寶,於是就把神拋諸腦後,從此不用... 阅读全帖
l***y
发帖数: 1166
15
来自主题: Military版 - 地球编年史
About the author of The Earth Chronicles, also from dust cover...
"Zecharia Sitchin was raised in Palestine, where he acquired a profound
knowledge of modern and ancient Hebrew, other Semitic and European languages
, the Old Testament, and the history and archaeology of the Near East. He
attended the London School of Economics and Political Science and graduated
from the University of London, majoring in economic history. A leading
journalist and editor in Israel for many years, he now lives and... 阅读全帖
S*********g
发帖数: 5298
16
取x=0 => b sin(m) = c sin(n)
取x=-m => -a sin(m) = c sin(n-m) = c sin(n) cos(m) - c cos(n) sin(m)
第1式放到第二式,消去 sin(m)
a + b cos(m) = c cos(n)
和第一式平方求和再开根号得:
c = (a^2+b^2+2ab cos(m)) ^(1/2)
代入第一式: sin(n) = b/c sin(m)
x******a
发帖数: 6336
17
first,
b* sin(x+m)=b* [sin(x)*cos(m)+cos(x)*sin(m)]= A*sin(x)+B*cos(x)
second,
a*sin(x)+ b*sin(x+m) = (a+A)*sin(x)+B*cos(x)
third,
(a+A)*sin(x)+B*cos(x)=\sqrt( (a+A)^2 +B^2) sin(x+n).
A**H
发帖数: 4797
18
来自主题: Parenting版 - 求助潮水等大牛
从娃的解释,基本上就是录像里面的意思。当然,细节上没有那么严密。
以前,我也总是要求娃必须在数学上能证明自己所说的结论,因为我在中国就是这么学
的:解答一个题目,不能稀里糊涂从第一步就得出了第三步的结论,因为第二步是不能
自证的,必须明白无误的说出来。后来发现似乎没有必要时时刻刻都这么要求,加上很
多时候是选择题,就觉得这样能很快的凭直觉指出答案也挺好。典型的例子就是娃两分
钟就猜出了椭圆面积公式。我觉得这样的直觉很好,但是没想到这样有可能成为民科。
。。LOL
娃用计算器一个一个摁给我看了y=sin(180/x)*x是怎么趋于pi的:
sin(180/1)*1=1
sin(180/2)*2=2
sin(180/6)*6=3
sin(180/10)*10=3.090
sin(180/100)*100=3.141
sin(180/10000)*10000=3.14159
我想,你指出来的是,娃在做一个“循环”论证,是吧?如果是的话,那就是娃后来和
我对于计算器是怎么算出sin(0.0018)来的讨论。我觉得计算器其实是事先知道pi值的
,所以算sin(0.0018),其实是用pi/100... 阅读全帖
s********d
发帖数: 364
19
来自主题: Joke版 - 大家来看看这道初中几何题
定理: 边1/sin角1=边2/sin角2=边3/sin角3
(a)由随意性,假设 (1): 角A>=角B>=角C
(b)显然根据定理 边B>=边C
下面要证明,边B<=边C,常识就不解释了
观察 ADE, BFD, CEF 三个小三角型
(c)DE/sin角A=AD/sin角AED,DF/sin角B=BF/sin角BDF, EF/sin角C=EC/sin角EFC
由这些小边大小相等,且大边大小也相等,可知 角AED >= 角BDF >= 角EFC
(d)由三角形内角和不变可知 角ADE <= 角BFD <= 角CEF
(e)再根据两条边一样,夹角越大,对应边越长可知,AE <= BD <= CF,那么AC <= AB
<= BC
(f) 根据(e)中的AC <= AB,即是 边B<=边C。
由(b)(f)可知 边B=边C
(g)根据全等三角形ADE和BFD,得到角A=角B,所以角A=角B=角C
C****i
发帖数: 1776
20
CHAPTER V
Of Providence
I. God the great Creator of all things doth uphold,[97] direct, dispose, and
govern all creatures, actions, and things,[98] from the greatest even to th
e least,[99] by his most wise and holy providence,[100] according to his inf
allible foreknowledge,[101] and the free and immutable counsel of his own wi
ll,[102] to the praise of the glory of his wisdom, power, justice, goodness,
and mercy.[103]
II. Although, in relation to the foreknowledge and decree of God, the first
... 阅读全帖
G*******s
发帖数: 4956
21
CHAPTER 6
OF THE FALL OF MAN, OF SIN, AND OF THE PUNISHMENT THEREOF
1. Our first parents, being seduced by the subtlety and temptation of Satan,
sinned, in eating the forbidden fruit. This their sin, God was pleased, acc
ording to his wise and holy counsel, to permit, having purposed to order it
to his own glory.
2. By this sin they fell from their original righteousness and communion wit
h God, and so became dead in sin, and wholly defiled in all the parts and fa
culties of soul and body.
3. Th... 阅读全帖
l**********t
发帖数: 5754
22
Chapter 2.2 Man’s State By Nature
We come therefore to Romans 5:12-21. In this great passage, grace is brought
into contrast with sin and the obedience of Christ is set against the
disobedience of Adam. It is placed at the beginning of the second section of
(Romans 5:12 to 8:39) with which we shall now be particularly concerned,
and its argument leads to a conclusion which lies at the foundation of our
further meditations. What is that conclusion? It is found in verse 19
already quoted: “For as ... 阅读全帖
l**********t
发帖数: 5754
23
Chapter 8.1 The Spirit Outpoured
Let us turn first to Acts chapter 2 verses 32 to 36: ”(32) This Jesus did
God raise up, whereof we all are witnesses. (33) Being therefore by the
right hand of God exalted, and having received of the Father the promise of
the Holy Ghost, he hath poured forth this, which ye see and hear. (34) For
David ascended not into the heavens: but he saith himself, The Lord said
unto my Lord, sit thou on my right hand, (35) Till I make thine enemies the
footstool of thy feet... 阅读全帖
l**********t
发帖数: 5754
24
Chapter 2.2 Man’s State By Nature
We come therefore to Romans 5:12-21. In this great passage, grace is brought
into contrast with sin and the obedience of Christ is set against the
disobedience of Adam. It is placed at the beginning of the second section of
(Romans 5:12 to 8:39) with which we shall now be particularly concerned,
and its argument leads to a conclusion which lies at the foundation of our
further meditations. What is that conclusion? It is found in verse 19
already quoted: “For as ... 阅读全帖
l**********t
发帖数: 5754
25
Chapter 8.1 The Spirit Outpoured
Let us turn first to Acts chapter 2 verses 32 to 36: ”(32) This Jesus did
God raise up, whereof we all are witnesses. (33) Being therefore by the
right hand of God exalted, and having received of the Father the promise of
the Holy Ghost, he hath poured forth this, which ye see and hear. (34) For
David ascended not into the heavens: but he saith himself, The Lord said
unto my Lord, sit thou on my right hand, (35) Till I make thine enemies the
footstool of thy feet... 阅读全帖
R*o
发帖数: 3781
26
来自主题: TrustInJesus版 - Study and Exposition of Romans 3:1-8
3:4 The answer to Paul’s question in v. 3 comes in v. 4: it is an emphatic
“absolutely not.” There is no way possible for the unbelief of the Jews to
nullify or render inoperative the faithfulness of God. God will be true to
what he has said. This will be demonstrated in the final judgment.
The purview in v. 4 does not exclude judgment in the present, but the focus
is on the final judgment when God will be shown to have been true all along
and every man, particularly the Jew, shown to have been ... 阅读全帖
R*o
发帖数: 3781
27
来自主题: TrustInJesus版 - Study and Exposition of Romans 3:1-8
G. Contribution of Passage to Systematic Theology
Romans 3:1-8 contributes to our understanding of sin (hamartiology) and how
God will deal with it. We are not to think for one minute that even though o
ur sin demonstrates the infinite righteousness of our perfect God that we ar
e therefore excused in some way from judgment or have thus been given licens
e to sin. Paul reserves strong language for those who follow this train of r
easoning. No matter how much glory God receives as a result of our... 阅读全帖
R*o
发帖数: 3781
28
来自主题: TrustInJesus版 - Study and Exposition of Romans 3:1-8
3:4 The answer to Paul’s question in v. 3 comes in v. 4: it is an emphatic
“absolutely not.” There is no way possible for the unbelief of the Jews to
nullify or render inoperative the faithfulness of God. God will be true to
what he has said. This will be demonstrated in the final judgment.
The purview in v. 4 does not exclude judgment in the present, but the focus
is on the final judgment when God will be shown to have been true all along
and every man, particularly the Jew, shown to have been ... 阅读全帖
R*o
发帖数: 3781
29
来自主题: TrustInJesus版 - Study and Exposition of Romans 3:1-8
G. Contribution of Passage to Systematic Theology
Romans 3:1-8 contributes to our understanding of sin (hamartiology) and how
God will deal with it. We are not to think for one minute that even though o
ur sin demonstrates the infinite righteousness of our perfect God that we ar
e therefore excused in some way from judgment or have thus been given licens
e to sin. Paul reserves strong language for those who follow this train of r
easoning. No matter how much glory God receives as a result of our... 阅读全帖
R*o
发帖数: 3781
30
by Dave Hunt
When You're Dead, Are You Dead?
Another major argument the Calvinist uses for Total Depravity is that by nat
ure we are all "dead in trespasses and in sins" (Ephesians 2:1; Colossians 2
:13). Sproul calls this statement "A predestination passage par excellence."
33 Continuing the fallacious equating of spiritual death to physical death,
Gordon H. Clark writes, "A dead man cannot exercise faith in Jesus Christ."
34 Of course, neither can a dead man reject Christ, or even sin. The ana... 阅读全帖
R*o
发帖数: 3781
31
by Dave Hunt
Leopard's Spots, Man's Skin Color - Like Sin?
That such natural deductions are the Calvinist's main weapon may explain why
their doctrines are so appealing to intellectuals. White continues:
Just as a person cannot change the color of their skin, or the leopard its s
pots, so the one who practices evil cannot break the bondage of sin and star
t doing good .... The New Testament continues the testimony of the radical d
epravity of man . . . Paul begins with a dreadfully long discussi... 阅读全帖
R*o
发帖数: 3781
32
来自主题: TrustInJesus版 - What Love is This?(93)预知不需要先预定
by Dave Hunt
Hear It From Calvin And Calvinists
In his classic, the five points of calvinism, Edwin H. Palmer writes, "Altho
ugh sin and unbelief are contrary to what God commands (His perceptive will)
, God has included them in His sovereign decree (ordained them, caused them
to certainly come to pass) .... How is it that a holy God, who hates sin, no
t only passively permits sin but also certainly and efficaciously decrees th
at sin shall be? Our infinite God presents us with some astounding t... 阅读全帖
m****s
发帖数: 18160
33
来自主题: TrustInJesus版 - [合集] 查经贴-使徒行传
☆─────────────────────────────────────☆
Dramaer (不要问我从那里来) 于 (Fri Oct 22 12:02:52 2010, 美东) 提到:
Act 1:1-11 Jesus Taken Up Into Heaven
1In my former book, Theophilus, I wrote about all that Jesus began to do and
to teach 2until the day he was taken up to heaven, after giving
instructions through the Holy Spirit to the apostles he had chosen. 3After
his suffering, he showed himself to these men and gave many convincing
proofs that he was alive. He appeared to them over a period of forty days
... 阅读全帖
s********n
发帖数: 1231
34
来自主题: TrustInJesus版 - 远志明柴玲谁该下地狱 曹长青
http://blog.sina.com.cn/u/3727008742
(七千人教会论坛转贴)
远志明柴玲谁该下地狱 曹长青
http://caochangqing.com/gb/newsdisp.php?News_ID=3722
曹长青
远志明和柴玲都在华人世界知名度很高,在这样两个来到美国后成了基督徒的公众人物
之间,发生了柴玲指控远志明二十多年前曾强暴她的事件,但主要华文媒体却几乎连理
都不理。导致这种现状的原因,首先是华文媒体远不够专业,再就是柴玲成为基督徒后
发表的“宽恕”六四屠杀者的言论引起了众怒,导致很多人对她可能是强暴受害者一事
也漠然。这当然是完全错误的,却也不无可理解之处。
第一,政治层面的对错、轻重。
但问题是,如果因政治观点,因“宽恕”言论而反感柴玲、认为她被强暴也活该的人们
,是否想过,被指控强奸的远志明为首的19人签署的《旧金山共识》的问题远比柴玲的
宽恕更严重!我们看这样的句子∶
“我们祈祷,愿上帝赐下爱和饶恕,使中国在和谐、和睦、和平中完成社会转型,重建
信用,得享平安,使公义如大水滔滔,使公平如江河滚滚。
我们祈祷,愿上帝赐福中国的执政掌权者,使他... 阅读全帖

发帖数: 1
35
遠志明柴玲誰該下地獄
曹長青
遠志明和柴玲都在華人世界知名度很高,在這樣兩個來到美國后成了基督徒的公眾人物
之間,發生了柴玲指控遠志明二十多年前曾強暴她的事件,但主要華文媒體卻幾乎連理
都不理。導致這種現狀的原因,首先是華文媒體遠不夠專業,再就是柴玲成為基督徒后
發表的“寬恕”六四屠殺者的言論引起了眾怒,導致很多人對她可能是強暴受害者一事
也漠然。這當然是完全錯誤的,卻也不無可理解之處。
第一,政治層面的對錯、輕重。
但問題是,如果因政治觀點,因“寬恕”言論而反感柴玲、認為她被強暴也活該的人們
,是否想過,被指控強奸的遠志明為首的19人簽署的《舊金山共識》的問題遠比柴玲的
寬恕更嚴重!我們看這樣的句子:
“我們祈禱,願上帝賜下愛和饒恕,使中國在和諧、和睦、和平中完成社會轉型,重建
信用,得享平安,使公義如大水滔滔,使公平如江河滾滾。
我們祈禱,願上帝賜福中國的執政掌權者,使他們更有治國的智慧與能力……
我們祈禱,願全能的上帝,賜福他的兒女,以百般的忍耐、溫柔、謙卑,順服上帝賜予
執政掌權者秉公行義的權柄。”
這都說些什麼呢?難道不是意向清晰的跟當局的調情嗎?這豈止是寬恕那個殺人政權,
... 阅读全帖
b********n
发帖数: 38600
36
来自主题: Military版 - 美国其它的原罪
America’s Other Original Sin
We have never reckoned with the bloody U.S. takeover of the Philippines, our

https://www.theamericanconservative.com/articles/americas-other-original-sin
-philippines/
1898 US Political Cartoon: U.S. President William McKinley is shown holding
the Philippines, depicted as a savage child, as the world looks on. The
implied options for McKinley are to keep the Philippines, or give it back to
Spain, which the cartoon compares to throwing a child off a cliff. (
Uncred... 阅读全帖
t*******r
发帖数: 22634
37
实际上很简单,把 (sin(x))' = cos(x),改写成
(sin(x))' = sin(x + (1/2)*pi)。
(小学生的话,就在笛卡尔坐标系里,画两条从原点
开始等长并且垂直的线段,从线段终点拉一条垂直落到
x 轴的线段,形成两个全等三角形,证明这个改写)。
然后因为微分算符的换元特性,所以就写成:
sin(x) => sin(x+(1/2)*pi) => sin(x + pi)
=> sin(x + (3/2)*pi) => sin(x) 回到起点
形成环结构。该环结构是四点构成的环结构。
对比一下,negation operator 其实也形成环结构。
但区别是,negation operator 形成的,是两点
构成的环结构。
如果还看不出来那俩 unary operator (在给定的
子空间上)的区别和联系的话。。。废柴。
s******1
发帖数: 969
38
来自主题: BrainTeaser版 - An integral
A==Integrate[Cos[x]^2*Log[-a*Cos[x] +Sqrt[1-a^2*Sin[x]^2]], {x, Pi, 2*Pi}]:
Introduce y=x-Pi so the range is [0,Pi].
Cos[x]=Cos[y+Pi]=-Cos[y]. Sin[x]=Sin[x+Pi]=-Sin[x].
A=Integrate[Cos[y]^2*Log[a*Cos[y] +Sqrt[1-a^2*Sin[y]^2]], {y,0, Pi}]
=Integrate[Cos[x]^2*Log[a*Cos[x] +Sqrt[1-a^2*Sin[x]^2]], {x,0, Pi}];
B==Integrate[Cos[x]^2*Log[-a*Cos[x] +Sqrt[1-a^2*Sin[x]^2]], {x, 0, Pi}];
Integrate[Cos[x]^2*Log[-a*Cos[x] +Sqrt[1-a^2*Sin[x]^2]], {x, Pi, 2*Pi}]
= A+B
=Integrate[Cos[x]^2*{Log[a*Cos[x] +Sqrt[1-
M********t
发帖数: 588
39
来自主题: Joke版 - 大家来看看这道初中几何题
设角BDF为角1,角AED为角2,角CFE为角3。
显然
<1+60= <2+60= <3+60= 又由正弦定理
Sin<2/Sin -> <1 < <2 (from (1))
-> Sin -> -> similarly -> =60)
60 -> similarly -> 60 (wrong again!)
So
G*******s
发帖数: 4956
40
来自主题: Belief版 - 摩门经证人
Is Mormonism Christian?:
A Comparison of Mormonism and Historic Christianity
Copyright ? 1999 Institute for Religious Research. All rights reserved.
Is Mormonism Christian? This may seem like a puzzling question to many Morm
ons as well as to some Christians. Mormons will note that they include the B
ible among the four books which they recognize as Scripture, and that belief
in Jesus Christ is central to their faith, as evidenced by their official n
ame, the Church of Jesus Christ of Latter-day... 阅读全帖
n********n
发帖数: 8336
41
来自主题: Belief版 - Bhagavad Gita
http://www.bhagavad-gita.us/summary-of-the-bhagavad-gita/
The Bhagavad-gita opens with blind King Dhritarashtra requesting his
secretary, Sanjaya, to narrate the battle between his sons, the Kauravas,
and their cousins, the Pandavas. Lord Krishna, the Supreme Personality of
Godhead, out of affection for His devotee, the Pandava prince Arjuna, has
agreed to drive his chariot. As Arjuna takes up his bow and prepares to
fight, he sees the sons of Dhritarashtra drawn in military array and
requests i... 阅读全帖
v********2
发帖数: 516
42
来自主题: TrustInJesus版 - 基督徒都信什么
Sins are equal. There's not one sin that is better or worse than the other.
If you don't believe, check the Bible. All Sins are Equal. All sins are
coming to Lord and be Judged in the final judgment.
All Babies or Infants are sinful. All human beings are sinful. So killing
which sinful people, and not killing other sinful people, is God's decision.
Killing his people means He's really mad, and the ones who were killed
received the punishment. The ones who were not killed really should THANK
HIM ... 阅读全帖
R*o
发帖数: 3781
43
来自主题: TrustInJesus版 - "Once Saved Always Saved" a dangerous delusion
Can you lose your salvation?
Many people fervently believe that once saved, they can never lose their sal
vation. I pray that those who do believe it will read the following with an
open heart and an open mind. Above all, I urge every reader to check each Sc
ripture presented and then check the context that the Scriptures are quote
d in by reading at least ten verses before and ten verses after.
I sincerely believe the 憃nce saved always savedconcept to be wrong. The i
mplication that once someon... 阅读全帖
C****i
发帖数: 1776
44
CHAPTER XXII
Of Lawful Oaths and Vows
I. A lawful oath is a part of religious worship,[443] wherein, upon just occ
asion, the person swearing solemnly calleth God to witness what he asserteth
, or promiseth, and to judge him according to the truth or falsehood of what
he sweareth.[444]
II. The name of God only is that by which men ought to swear, and therein it
is to be used with all holy fear and reverence.[445] Therefore, to swear va
inly, or rashly, by that glorious and dreadful Name; or, to ... 阅读全帖
l**********t
发帖数: 5754
45
chapter 12.4 The Light Of God And Knowledge
Of course, if one does not set out to serve the Lord whole-heartedly,
one does not feel the necessity for light. It is only when one has been
apprehended by God, and seeks to go forward with Him, that one finds
how necessary light is. There is a fundamental need of light in order
for us to know the mind of God; to know what is of the spirit and what
is of the soul; to know what is Divine and what is merely of man; to
discern what i... 阅读全帖
l**********t
发帖数: 5754
46
chapter 12.4 The Light Of God And Knowledge
Of course, if one does not set out to serve the Lord whole-heartedly,
one does not feel the necessity for light. It is only when one has been
apprehended by God, and seeks to go forward with Him, that one finds
how necessary light is. There is a fundamental need of light in order
for us to know the mind of God; to know what is of the spirit and what
is of the soul; to know what is Divine and what is merely of man; to
discern what i... 阅读全帖
s*y
发帖数: 933
47
来自主题: TrustInJesus版 - 刚出生的婴儿有什么罪?
Thanks for point out the word play on sin(s) and sinful nature as expected.
I believe "sinful nature" roughly means the tendency or capacity to commit
sins. Please let us know if you have another definition for this term.
So are you saying, when Adam was first created, he doesn't have a sinful
nature? In other words, was Adam created without the tendency or capacity
to commit sins?
Also, on the slightly different discussion on whether children should be
punished for the sins of the parent. Ho... 阅读全帖
R*o
发帖数: 3781
48
来自主题: TrustInJesus版 - Study and Exposition of Romans 1:18-32
E. Exposition Proper
The section 1:18-32 is part of the larger section of material in 1:18-3:20 (
cf. the teaching outline at the front of the book). The function of this mat
erial, as the for in 1:18 indicates, is to confirm that faith alone is the o
nly means of attaining the righteousness offered in the gospel in 1:17.
This is so because all men are depraved and cannot earn God’s salvation by
their own works or merit. The point of 1:18-32 is to show that the Gentiles
(primarily, though not ex... 阅读全帖
R*o
发帖数: 3781
49
来自主题: TrustInJesus版 - Study and Exposition of Romans 1:18-32
E. Exposition Proper
The section 1:18-32 is part of the larger section of material in 1:18-3:20 (
cf. the teaching outline at the front of the book). The function of this mat
erial, as the for in 1:18 indicates, is to confirm that faith alone is the o
nly means of attaining the righteousness offered in the gospel in 1:17.
This is so because all men are depraved and cannot earn God’s salvation by
their own works or merit. The point of 1:18-32 is to show that the Gentiles
(primarily, though not ex... 阅读全帖
R*o
发帖数: 3781
50
来自主题: TrustInJesus版 - Study and Exposition of Romans 3:9-20
C. Full Exegetical Outline
Idea: All men, Jew and Gentile alike, are sinners and will not be declared r
ighteous, i.e., attain a right standing with God, through works of the law.
I. The Jews are no better off than the Gentiles because all alike under sin
(3:9).
II. There is no one who has any standing before God on their own, for there
is no one who is righteous, understands or seeks God, or shows kindness; tog
ether all have become worthless (3:10-12).
A. There is no one who is righteous (3:10... 阅读全帖
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