(762)
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1 1,5 i,5
2 2,25 i,125
3 3,375 i,125
4 5,0625 i,265625
5 7,59375 i,51875
6 11,390625 i,8984375
i5 i125 i125 i265625 i518 i89 22
+ 15114040
− 1137845
162518851720
139761952023
Cæteriùm isthæc omnia & longè plura ex prop. 13, 15, & 16 Logarithmotechniæ nostræ apertè (illegible text) non magis considerando hyperbolam, quàm si ea nusquam in rerum (illegible text) extitisset. Quare frustra sunt, qui hyperbolam ad constructionem Logarithmorum vel hilum conferre autumant; imo Logarithmorum ope quadrare hyperbolam, verius est. Id quod exemplo ostendere haud pigebit. In diagrammate (Fig. 1.) sit A H 74305816 parium, qualium A I est 1, & oporteat invenire aream B I H F.
Opus est ad eam rem tabella subjecta, quæ continet Log-os naturales suprà acquisitos, in priori, columna ab 1 usque ad 9, in altera à 10 usque ad 1000000000.
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1 00000000000 02,30258508299
2 69314718052 04,60517018599
3 109861228860 06,90775527898
4 138629436104 09,21034037198
5 160943791232 11,51292546497
6 179175946912 13,81551055796
7 194591014904 16,11809565096
8 207944154156 18,42068074395
9 219722457720 20,72326583695
Tum prima figura numeri dati semper diftinguatur à sequentibus separatrice, hoc modo: 7,4305816, & ipsi primæ figuræ semper adjiciatur 1, ita conslantur, hoc loco, 8. Quærenda est nunc rationis 8 ad 7,4305816 mensura naturalis. Id ut fiat commodius dic: ut 8 ad 7,4305816; ita 1 ad 0,9288227, hunc quartum proportionalem auser ab 1, reliquum 0,0711773 voco potestatem primam, quæ ducenda est in se ita, ut in facto idem numerus partium extet, qui erat in ipso 0,0711773; productum 0,0050662 est potestas secunda, quæ rursus ducatur in primam 0,0711773, ut idem numerus partium extet, prodit 0,0003606, quæ est tertia potestas; & eodem modo invenitur-quarta 0,0000256, & (illegible text) 0,0000018. Deinde
