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

Table of contents

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[71.] PROP. VI. THEOREMATA.
[72.] SCHOLIUM.
[73.] PROP. VII. PROBLEMA. Oportet prædictæ ſeriei terminationem invenire.
[74.] PROP. VIII. PROBLEMA.
[75.] PROP. IX. PROBLEMA.
[76.] PROP. X. PROBLEMA.
[77.] CONSECTARIUM.
[78.] PROP. XI. THEOREMA.
[79.] SCHOLIUM.
[80.] PROP. XII. THEOREMA.
[81.] PROP. XIII. THEOREMA.
[82.] PROP. XIV. THEOREMA.
[83.] PROP. XV. THEOREMA.
[84.] PROP. XVI. THEOREMA.
[85.] PROP. XVII. THEOREMA.
[86.] PROP. XVIII. THEOREMA.
[87.] PROP. XIX. THEOREMA.
[88.] CONSECTARIUM.
[89.] PROP. XX. THEOREMA.
[90.] PROP. XXI. THEOREMA.
[91.] PROP. XXII. THEOREMA.
[92.] SCHOLIUM.
[93.] PROP. XXIII. THEOREMA.
[94.] PROP. XXIV. THEOREMA.
[95.] PROP. XXV. THEOREMA.
[96.] PROP. XXVI. THEOREMA.
[97.] PROP. XXVII. THEOREMA.
[98.] PROP. XXVIII. THEOREMA.
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
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182452VERA CIRCULI
Poteſtigitur abſque periculo erroris ſumi ſequens numerus
pro hyperbolæ ſectore, cujus numeri multiplices uſque ad
decem, diviſionis facilitandæ gratia in compoſitione logorith-
morum, hic ſubjicimus;
in magnis namque diviſionibus præ-
ſtat uti repetita diviſoris multiplicium ſubſtractione quam or-
dinaria diviſione, ut conſtat expertis arithmeticis.
Manifeſtum eſt hoc
11
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problema eodem
ferè modo poſſe reſol-
vi, etiamſi aſymptota
A O, A K, non ſint
conſtiruta ad angulum
rectum:
nos autem ita
fuppoſuimus, ut faci-
lior &
paratior eſſet
problematis uſus in doctrina logorithmica, quam primò
invenit nobiliſſimus noſter Neperus, &
quam nos (ni fal-
lor) ad ſummum perfectionis faſtigium nunc elevamus.
PROP. XXXIII. PROBLEMA.
Propoſiti cujuscunque numeri logorithmum invenire.
Eiſdem poſitis quæ in antecedente, manifeſtum eſt, poſita
22TAB. XLIV.
fig. 1.
I K unitate, M L eſſe decem:
poſita ergo I K unitate ſit
G H aſymptoto quoque A O parallela numerus propoſitus
cujus deſideratur logorithmus@ manifeſtum eſt ex data rectà
G H dari K F, &
ex præcedenti dari etiam ſpatium hyper-
bolicum G I K H, quod ſpatium hyperbolicum dico eſſe lo-
gorithmum numeri propoſiti G H, poſito ſpatio hyperbo-
lico L I K M logorithmo numeri denarii:
eſt enim (ex Gre-
gorio à S.
Vincentio) ſpatium G H K I in eadem ratione ad
ſpatium L M K I, in qua ratio G H ad I K eſt multiplicata
rationis L M ad I K;
ſed ratio G H ad I K eſt

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