首页 > 代码库 > NewtonPrincipia --- 公理或运动的定律 --- 系理二

NewtonPrincipia --- 公理或运动的定律 --- 系理二

NewtonPrincipia --- 公理或运动的定律 --- 系理二

 

自然哲学的数学原理>公理或运动的定律>系理II

平行四边形ABCD,那么:
直接的力AD由任意的力AB和BD合成,
直接的力AD可以任意分解为任意倾斜的力AB和BD


在垂直的重力中
从一个轮子的中心O伸出不等的半径OM、ON
由细线MA,NP支持着重量A和P,
过中心O引垂直于细线的直线KOL交细线于K和L
且以中心O和OK、OL中的较大者OL划一圈交细线MA与D
又做直线OD,AC平行与它,DC平行于它

 

证明:悬挂的重量之比是悬挂细线到轮子中心距离的反比

因为细线上的点K、L、D、是否属于轮子的平面并无差别
所以悬挂在K或L或D上的重量对轮子的效果是相同的

设重量A的力由细线AD表示,这个力被分为AC和CD
其中的AC直接的自中心拉半径OD,对轮子的运动没有作用
另一个力DC垂直的拉半径DO,犹如它垂直的拉等于OD的半径OL
这就是说,它与重量P有相同的作用

垂直拉OD的力与A的重力之比如同力DC比DA
由于三角形ADC、DOC相似,所以如同OK比OD
由于D、L在圆O的圆周上,所以如同OK比OL

这是天平、杠杆、绞盘所悉知的性质

下面的图是用SketchUp画的:

求值:在平衡时,斜面上的权p与另一侧的权A之比

权p等于权P,部分的被细线Np支撑,部分倚在倾斜的平面pG上
引pH、NH,前者垂直于地平线,后者垂直于平面pG
如果p向下的重力由线pH表示,这个力可以分解为pN、HN
如果某个平面pQ垂直于细线pN且截另一平面pG于平行于地平线的一条直线
这时,权p只倚在平面pQ、pG上它以力pH、HN垂直的压迫平面pQ、pG

如果平面pQ被除去,细线会被权p拉紧
细线的张力比垂线pN的张力如同pN比pH
因为权p等于权P,所以亦比垂线PN的张力如同pN比pH

权p和权A之比,由OK与OL的反比以及pH比pN的正比复合而成
这两个权对轮子的运动具有相同的效力,相互遏制达到平衡状态

 

以上内容引用自牛顿的《自然哲学的数学原理》,对它做了更适于理解的描述

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hosts文件和谷歌搜索引擎的使用

解决视频播放器kmplayer显示广告问题
C:\Windows\System32\drivers\etc\hosts
这个文件可以定义本地的域名解析,添加
127.0.0.1 player.kmpmedia.net
访问player.kmpmedia.net就会域名解析到127.0.0.1
这样,kmp广告找不到服务器就不会播放广告了

同样的,只要知道谷歌对应服务的ipv4地址就可以访问谷歌的服务了
因为其中有一些链接是用域名写的,
所以不修改本地域名映射文件的话,点击谷歌域名链接也是没有响应的

谷歌浏览器提供了图片搜索的功能,如图:

hosts文件如下:

# Copyright (c) 1993-2009 Microsoft Corp.## This is a sample HOSTS file used by Microsoft TCP/IP for Windows.## This file contains the mappings of IP addresses to host names. Each# entry should be kept on an individual line. The IP address should# be placed in the first column followed by the corresponding host name.# The IP address and the host name should be separated by at least one# space.## Additionally, comments (such as these) may be inserted on individual# lines or following the machine name denoted by a ‘#‘ symbol.## For example:##      102.54.94.97     rhino.acme.com          # source server#       38.25.63.10     x.acme.com              # x client host# localhost name resolution is handled within DNS itself.#    127.0.0.1       localhost#    ::1             localhost127.0.0.1    player.kmpmedia.net#################################################################################################===============================================================================================# Copyright (c) 1993-2009 Microsoft Corp.## This is a sample HOSTS file used by Microsoft TCP/IP for Windows.## This file contains the mappings of IP addresses to host names. Each# entry should be kept on an individual line. The IP address should# be placed in the first column followed by the corresponding host name.# The IP address and the host name should be separated by at least one# space.## Additionally, comments (such as these) may be inserted on individual# lines or following the machine name denoted by a ‘#‘ symbol.## For example:##      102.54.94.97     rhino.acme.com          # source server#       38.25.63.10     x.acme.com              # x client host# localhost name resolution is handled within DNS itself.#    127.0.0.1       localhost#    ::1             localhost#@abclite 2014.6.24#iOS/OSX/PC 32PRE NO PASSWORD#DO NOT ANDROID#Dropbox START108.160.165.147    dropbox.com108.160.165.147    www.dropbox.com108.160.166.140    client-lb.dropbox.com107.20.134.222    dl.dropbox.com107.20.134.222    dl-web.dropbox.com23.21.206.219    forums.dropbox.com108.160.165.211    notify0.dropbox.com108.160.165.211    notify1.dropbox.com108.160.165.211    notify2.dropbox.com108.160.165.211    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oi51.tinypic.com209.17.68.209    oi52.tinypic.com209.17.68.209    oi53.tinypic.com209.17.68.209    oi54.tinypic.com209.17.68.209    oi55.tinypic.com209.17.68.209    oi56.tinypic.com#---.---.---.---96.127.160.130    twitpic.com#96.127.160.130    m1.twitpic.com96.127.160.130    web1.twitpic.com96.127.160.130    web2.twitpic.com96.127.160.130    web3.twitpic.com96.127.160.130    web4.twitpic.com96.127.160.130    web5.twitpic.com96.127.160.130    web6.twitpic.com96.127.160.130    web7.twitpic.com96.127.160.130    web8.twitpic.com96.127.160.130    web9.twitpic.com96.127.160.130    web10.twitpic.com#Twitter END#Facebook Start127.0.0.1    ads.ak.facebook.com127.0.0.1    creative.ak.facebook.com127.0.0.1    creative.ak.fbcdn.net69.171.237.25    facebook.com69.171.237.25    www.facebook.com69.171.237.23    m.facebook.com69.171.237.25    d.facebook.com69.171.237.25    touch.facebook.com69.171.237.25    zh-CN.facebook.com69.171.237.25    ldap.thefacebook.com69.171.237.25    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apiblog.youtube.com61.19.1.54    help.youtube.com61.19.1.54    i.ytimg.com61.19.1.54    i1.ytimg.com61.19.1.54    i2.ytimg.com61.19.1.54    i3.ytimg.com61.19.1.54    i4.ytimg.com61.19.1.54    s.ytimg.com61.19.1.54    ytimg.l.google.com#Youtube??#UpLoad??61.19.1.109    uploads.clients.google.com61.19.1.109    uploads.client.google.com61.19.1.109    upload.clients.google.com61.19.1.109    upload.client.google.com74.125.203.117    upload.google.com74.125.203.117    upload.docs.google.com74.125.203.117    upload.drive.google.com74.125.203.117    upload.video.google.com74.125.203.117    upload.youtube.com74.125.203.117    uploads.stage.gdata.youtube.com74.125.203.117    uploads.code.google.com74.125.203.117    uploads.clients.google.com#Ingress??74.125.205.141    m-dot-betaspike.appspot.com74.125.205.141    betaspike.appspot.com74.125.205.141    chrometophone.appspot.com74.125.205.141    lfe-alpo-gm.appspot.com#Ingress??#GoogleAccounts??74.125.204.84    accounts.google.com74.125.204.84    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profiles.google.com61.19.1.54    reader.google.com61.19.1.54    sandbox.google.com61.19.1.54    sb.google.com61.19.1.54    sb.l.google.com61.19.1.54    sb-ssl.google.com61.19.1.54    sb-ssl.l.google.com61.19.1.54    scholar.google.com61.19.1.54    scholar.l.google.com61.19.1.54    script.google.com61.19.1.54    services.google.com61.19.1.54    sites.google.com61.19.1.54    sketchup.google.com61.19.1.54    sketchup.l.google.com61.19.1.54    spreadsheet.google.com61.19.1.54    spreadsheets.google.com61.19.1.54    spreadsheets.l.google.com61.19.1.54    spreadsheets0.google.com61.19.1.54    spreadsheets1.google.com61.19.1.54    spreadsheets2.google.com61.19.1.54    spreadsheets3.google.com61.19.1.54    spreadsheets4.google.com61.19.1.54    spreadsheets5.google.com61.19.1.54    spreadsheets6.google.com61.19.1.54    spreadsheets7.google.com61.19.1.54    spreadsheets8.google.com61.19.1.54    spreadsheets9.google.com61.19.1.54    spreadsheets-china.l.google.com61.19.1.54    suggestqueries.google.com61.19.1.54    suggestqueries.l.google.com61.19.1.54    support.google.com61.19.1.54    tbn0.google.com61.19.1.54    tbn1.google.com61.19.1.54    tbn2.google.com61.19.1.54    tbn3.google.com61.19.1.54    toolbar.google.com61.19.1.54    toolbarqueries.clients.google.com61.19.1.54    toolbarqueries.google.com61.19.1.54    toolbarqueries.l.google.com61.19.1.54    tools.google.com61.19.1.54    tools.l.google.com61.19.1.54    translate.google.com61.19.1.54    trENDs.google.com61.19.1.54    video.google.com61.19.1.54    video-stats.l.google.com61.19.1.54    voice.google.com61.19.1.54    wifi.google.com61.19.1.54    wifi.l.google.com61.19.1.54    wire.l.google.com61.19.1.54    writely.google.com61.19.1.54    writely.l.google.com61.19.1.54    writely-china.l.google.com61.19.1.54    writely-com.l.google.com61.19.1.54    www.l.google.com61.19.1.54    www2.l.google.com61.19.1.54    www3.l.google.com61.19.1.54    www4.l.google.com61.19.1.54    ytstatic.l.google.com61.19.1.54    appspot.com61.19.1.54    chrometophone.appspot.com61.19.1.54    evolutionofweb.appspot.com61.19.1.54    googcloudlabs.appspot.com61.19.1.54    gv-gadget.appspot.com61.19.1.54    magnifier.blogspot.com61.19.1.54    moderator.appspot.com61.19.1.54    newsfeed-dot-latest-dot-rovio-ad-engine.appspot.com61.19.1.54    productideas.appspot.com61.19.1.54    project-slingshot-gp.appspot.com61.19.1.54    r2303.latest.project-slingshot-hr.appspot.com61.19.1.54    r3085-dot-latest-dot-project-slingshot-gp.appspot.com61.19.1.54    r3091-dot-latest-dot-project-slingshot-gp.appspot.com61.19.1.54    r3101-dot-latest-dot-project-slingshot-gp.appspot.com61.19.1.54    r3269-dot-latest-dot-project-slingshot-gp.appspot.com61.19.1.54    r3432-dot-latest-dot-project-slingshot-hr.appspot.com61.19.1.54    r4681-dot-latest-dot-project-slingshot-hr.appspot.com61.19.1.54    r7647-dot-latest-dot-project-slingshot-hr.appspot.com61.19.1.54    wcproxyx.appspot.com61.19.1.54    www.appspot.com61.19.1.54    autoproxy-gfwlist.googlecode.com61.19.1.54    chromium.googlecode.com61.19.1.54    closure-library.googlecode.com61.19.1.54    earth-api-samples.googlecode.com61.19.1.54    gmaps-samples-flash.googlecode.com61.19.1.54    google-code-feed-gadget.googlecode.com61.19.1.54    imoutohost.googlecode.com61.19.1.54    smarthosts.googlecode.com61.19.1.54    huhamhire-hosts.googlecode.com61.19.1.54    blogsearch.google.cn61.19.1.54    g.cn61.19.1.54    www.g.cn61.19.1.54    ditu.google.cn61.19.1.54    maps.google.cn61.19.1.54    gg.google.cn61.19.1.54    id.google.cn61.19.1.54    maps.gstatic.cn61.19.1.54    m.google.cn61.19.1.54    mt.google.cn61.19.1.54    mt0.google.cn61.19.1.54    mt1.google.cn61.19.1.54    mt2.google.cn61.19.1.54    mt3.google.cn61.19.1.54    news.google.cn61.19.1.54    scholar.google.cn61.19.1.54    translate.google.cn61.19.1.54    www.google.cn61.19.1.54    www.gstatic.cn61.19.1.54    accounts.google.com.hk61.19.1.54    blogsearch.google.com.hk61.19.1.54    books.google.com.hk61.19.1.54    clients1.google.com.hk61.19.1.54    desktop.google.com.hk61.19.1.54    encrypted.google.com.hk61.19.1.54    groups.google.com.hk61.19.1.54    gxc.google.com.hk61.19.1.54    id.google.com.hk61.19.1.54    images.google.com.hk#61.19.1.54    m.google.com.hk61.19.1.54    maps.google.com.hk61.19.1.54    news.google.com.hk61.19.1.54    picasaweb.google.com.hk61.19.1.54    plus.url.google.com.hk61.19.1.54    scholar.google.com.hk61.19.1.54    toolbar.google.com.hk61.19.1.54    toolbarqueries.google.com.hk61.19.1.54    translate.google.com.hk61.19.1.54    wENDa.google.com.hk61.19.1.54    www.google.com.hk61.19.1.54    accounts.google.com.tw61.19.1.54    blogsearch.google.com.tw61.19.1.54    books.google.com.tw61.19.1.54    clients1.google.com.tw61.19.1.54    desktop.google.com.tw61.19.1.54    encrypted.google.com.tw61.19.1.54    groups.google.com.tw61.19.1.54    gxc.google.com.tw61.19.1.54    id.google.com.tw61.19.1.54    images.google.com.tw#61.19.1.54    m.google.com.tw61.19.1.54    maps.google.com.tw61.19.1.54    news.google.com.tw61.19.1.54    picasaweb.google.com.tw61.19.1.54    plus.url.google.com.tw61.19.1.54    scholar.google.com.tw61.19.1.54    toolbar.google.com.tw61.19.1.54    toolbarqueries.google.com.tw61.19.1.54    translate.google.com.tw61.19.1.54    www.google.com.tw61.19.1.54    accounts.google.com.sg61.19.1.54    blogsearch.google.com.sg61.19.1.54    books.google.com.sg61.19.1.54    clients1.google.com.sg61.19.1.54    desktop.google.com.sg61.19.1.54    encrypted.google.com.sg61.19.1.54    groups.google.com.sg61.19.1.54    gxc.google.com.sg61.19.1.54    id.google.com.sg61.19.1.54    images.google.com.sg#61.19.1.54    m.google.com.sg61.19.1.54    maps.google.com.sg61.19.1.54    news.google.com.sg61.19.1.54    picasaweb.google.com.sg61.19.1.54    plus.url.google.com.sg61.19.1.54    scholar.google.com.sg61.19.1.54    toolbar.google.com.sg61.19.1.54    toolbarqueries.google.com.sg61.19.1.54    translate.google.com.sg61.19.1.54    www.google.com.sg61.19.1.54    accounts.google.co.jp61.19.1.54    blogsearch.google.co.jp61.19.1.54    books.google.co.jp61.19.1.54    clients1.google.co.jp61.19.1.54    desktop.google.co.jp61.19.1.54    encrypted.google.co.jp61.19.1.54    groups.google.co.jp61.19.1.54    gxc.google.com.co.jp61.19.1.54    id.google.com.co.jp61.19.1.54    images.google.co.jp#61.19.1.54    m.google.com.co.jp61.19.1.54    maps.google.co.jp61.19.1.54    news.google.co.jp61.19.1.54    picasaweb.google.co.jp61.19.1.54    plus.url.google.co.jp61.19.1.54    scholar.google.co.jp61.19.1.54    toolbar.google.co.jp61.19.1.54    toolbarqueries.google.co.jp61.19.1.54    translate.google.co.jp61.19.1.54    www.google.co.jp61.19.1.54    android.googlesource.com61.19.1.54    auth.keyhole.com61.19.1.54    chrome.angrybirds.com61.19.1.54    developer.chrome.com61.19.1.54    domains.googlesyndication.com61.19.1.54    earthengine.googlelabs.com#61.19.1.54    feeds.feedburner.com61.19.1.54    g.co61.19.1.54    gmail.com61.19.1.54    goo.gl61.19.1.54    listen.googlelabs.com61.19.1.54    m.gmail.com61.19.1.54    m.googlemail.com61.19.1.54    ngrams.googlelabs.com61.19.1.54    ssl.google-analytics.com61.19.1.54    www.gmail.com61.19.1.54    www.googleadservices.com61.19.1.54    www.google-analytics.com#61.19.1.54    www-google-analytics.l.google.com61.19.1.54    www.googlelabs.com61.19.1.54    www.googlesource.com61.19.1.54    chatenabled.mail.google.com61.19.1.54    panoramio.com61.19.1.54    www.panoramio.com61.19.1.54    static.panoramio.com#61.19.1.54    www.blogger.com61.19.1.54    googleblog.blogspot.com61.19.1.54    googlechinablog.blogspot.com#61.19.1.54    1.bp.blogspot.com#61.19.1.54    2.bp.blogspot.com#61.19.1.54    3.bp.blogspot.com#61.19.1.54    4.bp.blogspot.com#Google Services END#+END#===============================================================================================################################################################################################

 

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kongdongyang

2014/9/21

 

NewtonPrincipia --- 公理或运动的定律 --- 系理二