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

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[61.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA AUTHORE JACOBO GREGORIO. LECTORI GEOMETRÆ SALUTEM.
Page: 134
[62.] DEFINITIONES.
Page: 139
[63.] PETITIONES.
Page: 141 (414)
[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
Page: 142 (415)
[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.
Page: 142 (415)
[66.] PROP. II. THEOREMA. Dico trapezia A B F P, A B I P ſimul, eſſe ad du- plum trapezii A B I P, ſicut trapezium A B F P ad polygonum A B D L P.
Page: 143 (416)
[67.] PROP. III. THEOREMA. Dico triangulum B A P, & trapezium A B I P ſimul, eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.
Page: 144 (417)
[68.] PROP. IV. THEOREMA. Dico polygonum A B E I O P eſſe medium pro- portionale inter polygonum A B D L P & trapezium A B I P.
Page: 144 (417)
[69.] PROP. V. THEOREMA.
Page: 145 (418)
[70.] SCHOLIUM.
Page: 146 (419)
[71.] PROP. VI. THEOREMATA.
Page: 147 (420)
[72.] SCHOLIUM.
Page: 148 (421)
[73.] PROP. VII. PROBLEMA. Oportet prædictæ ſeriei terminationem invenire.
Page: 150 (423)
[74.] PROP. VIII. PROBLEMA.
Page: 152 (425)
[75.] PROP. IX. PROBLEMA.
Page: 153 (426)
[76.] PROP. X. PROBLEMA.
Page: 154 (427)
[77.] CONSECTARIUM.
Page: 155 (428)
[78.] PROP. XI. THEOREMA.
Page: 156 (429)
[79.] SCHOLIUM.
Page: 159 (432)
[80.] PROP. XII. THEOREMA.
Page: 161 (434)
[81.] PROP. XIII. THEOREMA.
Page: 161 (434)
[82.] PROP. XIV. THEOREMA.
Page: 162 (435)
[83.] PROP. XV. THEOREMA.
Page: 162 (435)
[84.] PROP. XVI. THEOREMA.
Page: 163 (436)
[85.] PROP. XVII. THEOREMA.
Page: 164 (437)
[86.] PROP. XVIII. THEOREMA.
Page: 164 (437)
[87.] PROP. XIX. THEOREMA.
Page: 165 (438)
[88.] CONSECTARIUM.
Page: 165 (438)
[89.] PROP. XX. THEOREMA.
Page: 165 (438)
[90.] PROP. XXI. THEOREMA.
Page: 166 (439)
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34328THEOR. DE QUADRAT. HYPERB. &c.
Eſto jam denique ſector D A B C ſemicirculo major, &
11TAB. XXXVI.
Fig. 5. ponantur ea quæ priùs, & perficiatur circulus B A F C,
& totius diameter ſit B D F, in qua erit quoque centrum
grav. ſectoris reliqui D A F C , quot ſit G.
228. lib. 1.
Arch. de
Æquip.
Quia igitur circuli totius centrum gravitatis eſt D, & duorum
ſectorum centra grav. E & G, erit ſicut ſector D A B C, ad ſecto-
rem D A F C, id eſt, ſicut arcus A B C ad arcum A F C, ita
G D ad D E : verum ut arcus A F C ad {2/3} A C, ita eſt D 338. lib. 1.
Arch. de
Æquip. ad D G, ſicuti modò oſtenſum eſt; ergo ex æquali in pro-
portione perturbata, ſicut arcus A B C ad {2/3} A C, ita erit
D F vel B D ad D E . Conſtat itaque quod in 4423. lib. 5.
Elem. lo & quolibet circuli ſectore & c. quod erat demonſtrandum.
ἘΞἘΤΑΣΙΣ
CYCLOMETRIÆ
CLARISSIMI VIRI,
GREGORII à S. VINCENTIO, S. J.
Editæ Anno D. cIↄ Iↄc XLVII.
ANte quinquennium circiter Vir eruditiſſimus &
Geometriâ celeberrimus, Gregorius à S. Vin-
centio, quatuor modos propoſuit quadrandi Cir-
culum, unum vero eorum etiam Quadraturæ Hy-
perboles applicavit: quem cæteris potiorem ab
ipſo exiſtimari ex multis indiciis colligere licet. Unum eſt
hoc ipſum quod duas diverſarum figurarum quadraturas per
eundem hunc demonſtravit; alterum quod evidentior multò
ſit hic modus quam reliqui tres, ideoque minus errori obno-
xius videri debuerit; nonnullum etiam quod primo eum lo-
co produxit; Et denique hoc maximum eſt, quod in iis quæ
@d lectorem in principio totius operis præfatur, ubi ſuæ

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