Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of figures

[151] Fig. 32.* 17. Iun.

[152] Fig. 33.* 19. Oct.

[153] Fig. 34.* 21. Oct.

[154] Fig. 35.* 9. Nov.

[155] Fig. 36.* 27. Nov.

[156] Fig. 37.* 16. Dec.

[157] Fig. 38.* 18. Ian. 1657.

[158] Fig. 39.* 29. Mart.

[159] Fig. 40.* 30. Mart.

[160] Fig. 41.* 18. Maii.

[161] Fig. 42.* 19. Maii.

[162] Fig. 43.* 17. Dec.

[163] Fig. 44.* 18. Dec.

[164] Fig. 45.* 27. Dec.

[165] Fig. 46.* 11. Mart 1658.

[166] Fig. 47.* 16. Mart.

[167] Fig. 48.* 23. Mart.

[168] Fig. 49.* 3. Apr.

[169] Fig. 50.* 10. Nov.

[170] Fig. 51.* 16. Ian. 1659.

[171] Fig. 52.12. Febr. *

[172] Fig. 53.* 24. Febr.

[173] Fig. 54.25. Febr. *

[174] Fig. 55.14. Mart. *

[175] Fig. 56.16. Mart. *

[176] Fig. 57.* 21. Mart.

[177] Fig. 58.* 22. Mart.

[178] Fig. 59.26. Mart. *

[179] Pag. 574.TAB. XLIX.Fig. 2.

[180] Fig. 1.C K O B H N G M S * F D A L E

156429ET HYPERBOLÆ QUADRATURA. omnes ſeriei convergentis terminationem eodem modo eſſe
compoſitam ex terminis convergentibus primis quo ex termi-
nis convergentibus ſecundis, tertiis, vel quartis, & c.

PROP. XI. THEOREMA.

Dico ſectorem circuli, ellipſeos vel hyperbolæ A B I P
11TAB. XLIII.
Fig. 1. 2. 3. non eſſe compoſitum analyticè à triangulo
A B P & trapezio A B F P.

Ponatur triangulum A B P a & trapezium A B F P b: ma-
nifeſtum eſt ex prædictis trapezium A B I P eſſe Vqab &
polygonum A B D L P {2 ab/a + Vqab}, item ſectorem A B I P eſſe
hujus ſeriei convergentis terminationem. ut ex ſeriei termi-
nis auferantur ſigna radicis & fractionis, pro a & b primis
ſeriei terminis convergentibus, hoc eſt pro triangulo A B P
& trapezio A B F P ponantur a3 + a2 b & ab2 + b3; erunt-
que ſecundi ſeriei termini convergentes, hoc eſt trapezium
A B I P & polygonum A B D L P, ba2 + b2 a & 2 b 2 a, di-
co ſeriei convergentis (cujus primi termini convergentes ſunt
a3 + a2b, ab2 + b3 & ſecundi ſunt ba2 + b2 a, 2 b2 a) termina-
tionem non eſſe compoſitam analyticè a terminis a3 + a2 b,
ab2 + b3: ſi enim componatur prædicta terminatio analyticè a
terminis convergentibus a3 + a2b, ab2 + b3; componetur etiam
eadem terminatio analyticè & eodem omnino modo à termi-
nis convergentibus ba2 + b2a, 2b2a; & proinde eadem quan-
titas, nempe prædicta terminatio, eodem modo componitur
analyticè ex terminis a3 + a2b, ab2 + b3, quo componitur ex
terminis ba2 + b2a, 2b2a,
22
a3 + a2b # ab2 + b3.
ba2 + b2 a # 2b2a
ſed nulla quantitas poteſt
eodem modo analyticè com-
poni ex terminis a3 + a2b,
ab2 + b3, quo componitur
ex terminis ba2 + b2a, 2b2a, quod ſic demonſtro. ſi analy-
ticè componeretur quantitas ex terminis a3 + a2b, ab2 + b3

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