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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72360CHRISTIANI HUGENII
Theor. IV. Prop. IV.
Omnis circuli portio, ſemicirculo minor, minor
eſt duabus tertiis trianguli eandem cum ipſa
baſin babentis, & latera portionem contingentia.
Eſto circuli portio, ſemicirculo minor, A B C, & contin-
11TAB. XXXVIII.
Fig. 4. gant ipſam ad terminos baſis rectæ A D, C D, quæ con-
veniant in puncto D. Dico Portionem A B C minorem eſſe
duabus tertiis trianguli A D C. Ducatur enim E F quæ por-
tionem contingat in vertice B, & inſcribatur ipſi triangu-
lum maximum A B C. Quum igitur triangulum E D F ma-
jus ſit dimidio trianguli A B C , manifeſtum eſt ab 22per. 2. huj. partem abſcindi poſſe, ita ut reliquum tamen majus ſit di-
midio dicti A B C trianguli. Sit igitur hoc pacto abſciſſum
triangulum E D G. Et ducantur porro rectæ H I, K L,
quæ portiones reliquas A M B, B N C in verticibus ſuis
contingant, ipſiſque portionibus triangula maxima inſcri-
bantur. Idemque prorſus circa reliquas portiones fieri intel-
ligatur, donec tandem portiones reſiduæ ſimul minores ſint
quam duplum trianguli E D G. Erit igitur inſcripta portio-
ni figura quædam rectilinea, atque alia circumſcripta. Et
quoniam triangulum E G F majus eſt dimidio trianguli
A B C; & rurſus triangula H E I, K F L, majora quam
dimidia triangulorum A M B, B N C; idque eadem ſem-
per ratione in reliquis locum habet, ut triangula ſuper por-
tionum verticibus conſtituta, eorum quæ intra portiones i-
pſas deſcripta ſunt, majora ſint quam ſubdupla: apparet tri-
angula omnia extra portionem poſita etiam abſque triangu-
lo E G D majora ſimul eſſe quam dimidia triangulorum o-
mnium intra portionem deſcriptorum. Atqui ſegmentorum in
portione reliquorum triangulum quoque E G D majus eſt
quam ſubduplum. Ergo triangulum E D F ſimul cum reli-
quis triangulis, quæ ſunt extra portionem, majus erit dimi-
dio portionis totius A B C. Quare multo magis ſpatium

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