![{\displaystyle \scriptstyle +{\frac {3}{256\alpha '}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e439c8f7f99750e18c327fc79c6de025ee5a6123)
![{\displaystyle \scriptstyle +{\frac {3}{128\alpha '^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2313ed6ecf59fbf375501237ef75e6a6b4b41ffc)
![{\displaystyle \scriptstyle +{\frac {1}{16\alpha '^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7587100f1e7e442855ba7f85efd27174a0ffbcde)
![{\displaystyle \scriptstyle +{\frac {3}{8\alpha '^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72b7120e2aefdb04692c475319ec61e7a4b2442f)
![{\displaystyle \scriptstyle +{\frac {3}{2\alpha '^{5}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c33d317d278a9a57ef37836d5c2c908797543d0)
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![{\displaystyle \scriptstyle {\frac {x^{10}}{r^{9}}}+{\frac {7}{1024\alpha '}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9ff20c626c741433352514afd7da3a226fcf7b8)
![{\displaystyle \scriptstyle +{\frac {3}{256\alpha '^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec8955a44efbe77d861782a028ae1cfb48f49fdc)
![{\displaystyle \scriptstyle +{\frac {3}{128\alpha '^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/be3cc31261dc73a9ff1b1cf7c7b294f5afcabd88)
![{\displaystyle \scriptstyle +{\frac {1}{16\alpha '^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/201f167611c9909d6df1a612466de1abfde8fec8)
![{\displaystyle \scriptstyle +{\frac {3}{8\alpha '^{5}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27549af4fd6540d45416a4942ca30d474a1b26a2)
![{\displaystyle \scriptstyle -{\frac {3}{2\alpha '^{6}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/631a9bd5a658738805f37573152bc71a1f0f843d)
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![{\displaystyle \scriptstyle {\frac {x^{12}}{r^{11}}}+{\frac {9}{2048\alpha '}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18787097dad87518002012f6c56993853c62a3e8)
![{\displaystyle \scriptstyle +{\frac {7}{1024\alpha '^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3689dff28ec9ab18e2ae18a259fcb070b8075623)
![{\displaystyle \scriptstyle +{\frac {3}{256\alpha '^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d128c3f29bf8b17edb231edb6dea0633aeb4fc11)
![{\displaystyle \scriptstyle +{\frac {3}{128\alpha '^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/99c792821c89e1f4a2cb36fc6006b3f0daf43b5f)
![{\displaystyle \scriptstyle +{\frac {1}{16\alpha '^{5}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4884d3a19c884a6293e9d2ec7ee8c73637b920ba)
![{\displaystyle \scriptstyle -{\frac {3}{8\alpha '^{6}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32796d0b5ad90745720289ac6755cd25f58f4cdc)
![{\displaystyle \scriptstyle -{\frac {3}{2\alpha '^{7}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86e7b0e30caff44bdc560f200eaabb526eb326d3)
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Hiernach wird
![{\displaystyle \scriptstyle \int \limits _{-r}^{+r}y'dx=r^{2}\left\{{\frac {1}{\alpha '}}\left[2-1+{\frac {3}{20}}+{\frac {1}{56}}+{\frac {1}{192}}+{\frac {3}{1408}}+{\frac {7}{6656}}+{\frac {3}{5120}}\right]\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32ca4b98f31039239f8d35fa41f2fe2e3358460a)
![{\displaystyle \scriptstyle +{\frac {1}{\alpha '^{2}}}\left[{\frac {2}{3}}-{\frac {3}{5}}+{\frac {3}{28}}+{\frac {1}{72}}+{\frac {3}{704}}\dots \right]+{\frac {1}{\alpha '^{3}}}\left[{\frac {2}{5}}-{\frac {3}{7}}+{\frac {1}{12}}\dots \right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc8ef2cdce62fcf89e76b1942201441df39e569b)
![{\displaystyle \scriptstyle \left.+{\frac {1}{\alpha '^{4}}}\left[{\frac {2}{7}}-{\frac {1}{3}}+{\frac {3}{44}}\dots \right]\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7e32b1382e16d39ddd3514d909ac594a1bc243e7)
etc.
![{\displaystyle \scriptstyle =r^{2}\left[{\frac {1,17711}{\alpha '}}+{\frac {0,1917}{\alpha '^{2}}}+{\frac {0,054}{\alpha '^{3}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c649f900cbbb947536e314208e6e32eca47160f0)
= 0,11869r².
Der Halbkreis ist = ½r²π, mithin verhält sich NAn : NeFn = 1,57090 : 0,11869 = 794,1 : 60.
No. 262. S. 437. (Fig. 199.) Weil TH² = TS · TK ist, wird SK : ST = SK :
= TK · TK : TH² = (TK – TS)TK : TH² = TK² – TH² : TH² = (TK + TK)(TK – TH) : TH² endlich TK : ST = MH · HK : TH².
No. 263. S. 437. (Fig. 199.) Setzt man nämlich FG = Y, BG = y, GT = x, HT = h, KT = a; so ist y² =
(a² – x²), Y² = a² – x², mithin
.
No. 264. S. 438. (Fig. 199.) Nach 1. wird nämlich TH : TK =
.
No. 265. S. 438. (Fig. 199.) Setzet man, wie in Bem. 264. BG = y, FG = Y, TG = x, ferner
FTG = β und
FTB = α – β = γ; so ist allgemein tang α =
, tang β =
, tang γ =
. Wenn aber