189459ET HYTERBOLÆ QUADRATURA.
PROP. XXXIV. PROBLEMA.
Ex dato logorithmo invenire ejus
numerum.
numerum.
Ex demonſtratis manifeſtum eſt hoc problema idem eſſe
11TAB. XLIV.
fig. 1. ac ſi quis proponeret; ex dato ſpatio hyperbolico, &
una recta uni aſymptotorum parallela illud comprehenden-
te, alteram invenire idem ſpatium comprehendentem, &
eidem aſymptoto parallelam. Conſideretur ex quot notis
arithmeticis conſtet logorithmus denarii arbitrarius; & ſuma-
tur logorithmi vel ſpatii dati talis pars aliquota nempe ſpa-
tium L I K M, ut pentagoni ſpatio L I K M regulariter cir-
cumſcripti, & hexagoni eidem regulariter inſcripti toties
multiplicia, quoties ſpatium datum multiplex eſt ſpatii
L I K M, concordent in tot notis arithmeticis, quot conti-
net radix quadrata logorithmi arbitrarii; hoc enim facile fie-
ri poteſt ex inſpectione tabellæ 32 hujus: datur ergo ſpatii
L I K M menſura & recta I K unitas ex ſuppoſitione. Sit
L M, z; ſicut in hujus 32 datur pentagonum ſpatio L I K M
regulariter circumſcriptum & hexagonum eidem regulariter
inſcriptum, inter quæ ſpatium datum L I K M eſt ſecunda
duarum mediarum arithmeticè continuè proportionalium;
& ideo duplum haxagoni una cum pentagono æquatur triplo
ſpatii, cujus æquationis reſolutio manifeſtat ignotam z ſeu
numerum L M, cujus toties multiplicatus, quoties ſpatium
L I K M eſt ſubmultiplex ſpatii vel logorithmi dati, eſt nu-
merus quæſitus, quem invenire oportuit.
11TAB. XLIV.
fig. 1. ac ſi quis proponeret; ex dato ſpatio hyperbolico, &
una recta uni aſymptotorum parallela illud comprehenden-
te, alteram invenire idem ſpatium comprehendentem, &
eidem aſymptoto parallelam. Conſideretur ex quot notis
arithmeticis conſtet logorithmus denarii arbitrarius; & ſuma-
tur logorithmi vel ſpatii dati talis pars aliquota nempe ſpa-
tium L I K M, ut pentagoni ſpatio L I K M regulariter cir-
cumſcripti, & hexagoni eidem regulariter inſcripti toties
multiplicia, quoties ſpatium datum multiplex eſt ſpatii
L I K M, concordent in tot notis arithmeticis, quot conti-
net radix quadrata logorithmi arbitrarii; hoc enim facile fie-
ri poteſt ex inſpectione tabellæ 32 hujus: datur ergo ſpatii
L I K M menſura & recta I K unitas ex ſuppoſitione. Sit
L M, z; ſicut in hujus 32 datur pentagonum ſpatio L I K M
regulariter circumſcriptum & hexagonum eidem regulariter
inſcriptum, inter quæ ſpatium datum L I K M eſt ſecunda
duarum mediarum arithmeticè continuè proportionalium;
& ideo duplum haxagoni una cum pentagono æquatur triplo
ſpatii, cujus æquationis reſolutio manifeſtat ignotam z ſeu
numerum L M, cujus toties multiplicatus, quoties ſpatium
L I K M eſt ſubmultiplex ſpatii vel logorithmi dati, eſt nu-
merus quæſitus, quem invenire oportuit.
Hoc problema idem eſt cum hujus 8, ſed aliter genera-
lius & methodo plerumque minus operoſa hic reſolu-
tum.
lius & methodo plerumque minus operoſa hic reſolu-
tum.
Tom. II. Mmm