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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page |< < (428) of 568 > >|
155428VERA CIRCULI ſequentes Vqab, {aa. /Vqab} ſumma terminorum convergentium a + b
multiplicata in terminum convergentem primum a efficit
aa + ab: & ſumma terminorum convergentium immediate ſe-
quentium nempe Vqab + {aa/Vqab} multiplicata in primum terminum
convergentem Vqab efficit etiam aa + ab; ex his invenienda ſit ſe-
riei propoſitæ terminatio. manifeſtum eſt quantitatem aa + ab
eodem modo fieri à terminis convergentibus a, b, quo à termi-
nis convergentibus immediatè ſequentibus Vqab, {aa/Vqab: } & quo-
niam quantitates a, b, indefinitæ ponuntur pro quibuslibet to-
tius ſeriei terminis convergentibus, evidens eſt ſummam quo-
rumcunque terminorum convergentium propoſitæ ſeriei mul-
tiplicatam in primum terminum convergentem efficere quan-
titatem æqualem illi, quæ fit à ſumma terminorum conver-
gentium immediatè ſequentium multiplicata etiam in primum
ſuum terminum convergentem; cumque duo termini conver-
gentes duos terminos convergentes ſemper immediatè ſe-
quuntur, manifeſtum eſt ſummam duorum quorumlibet ter-
minorum convergentium multiplicatam in primum ſemper
efficere eandem quantitatem nempe aa + ab, atque ultimi ter-
mini convergentes ſunt æquales, & proinde ſit ultimus ille
terminus ſeu ſeriei terminatio z, quæ ſibi addita & in ſum-
mam multiplicata efficit 2 zz, quæ quantitas debet eſſe æqua-
lis quantitati aa + ab, & æquatione reſoluta dabitur z ſeu ſeriei
terminatio {Vq aa + ab,/2} quam invenire oportuit.
Et proinde ad inveniendam cujuscunque ſeriei convergen-
tis terminationem; opus eſt ſolummodo invenire quantitatem
eodem modo compoſitam ex terminis convergentibus primis,
quo componitur eadem quantitas ex terminis convergentibus
ſecundis.
CONSECTARIUM.
Quoniam non refert in problemate ſive termini conver-
gentes a, b, ſint primi, ſecundi, vel tertii & c; manifeſtum

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