Page:Philosophical Transactions - Volume 003.djvu/139

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(762)

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

1625188517/20

1397619520/23


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.

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

Potestas