Page:Philosophical Transactions - Volume 003.djvu/138

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Similes ordines ȧ 3rio, 4rio, & quovis alio numero derivari possunt, suas quisque rationes exhibiturus.


Acquisito Log-o 10rii, consicienda est conscienda est statim tabell reducendorum Logorum naturalium ad Tabulares, ut qævis ratio, simul ac inventa est, reducatur ad mensuram tabularium; ita enim Log-i compositorum, quorum ope ad primorum Log-os descenditur, simul sient Tabulares absque reductione.

Fiat igitur, ut Log-us 10rii non-tabularis 1302585, ad tabularem 10000000; ita 1, ad 4,3429448. Hic numerus bis, ter, quater & pluries sumptus constituit tabellam reducendorum Log-orum namralium ad tabulares, quam hic fubjectam vides.

1 043429448190

2 086858896380

3 130288344570

4 173717792761

5 217147240951

6 260576689141

7 304006137332

8 347435585522

9 390865033712

Hujus igitur ope tabellæ, rationis 98/100 mensura naturalis 20202707316 reducitur ad tabularem hoc modo:

2 086858896381

0 0

2 0868588964

0 0

2 08685890

7 3040061

0 0

7 30401

3 1303

1 043

6 26

87739243069

Tum à Log-0 100rii auseratur rationis 98/100 mensura festat unde ablato Log-211 restat —— —— ———

20000000000000

87739243069

19912260756031 = L 98

16901960800291 = L 99

8450980400145 = L 7

cujus semis ——— ——

Item rationis 100/102 mensura naturalis 19802627296 reductam sit 86001717619.

Ergo ja Log-0 100rii adde rationis 100/102 mensurā sit —— ——— ——

20000000000000

86001717619

20086001717619 = L 102

7781512503836

12304489213783 = L 17

unde ablato Log-0 6rii restat {[bar|3}} ———

Hic tabula numerorum primorum egregium usum præstare potest.


Sed & ejusdem primi 17 Log-um absque ambage invenire datur, dicendo: 20. 17:: 10. 8|5; tum differentiæ inter 10 & 8|5 (nimirum 1|5) sumendo quadraci semissem, cubi trientem, &c. tractandoque istum ordinem, ut suprà, inveniemus simul Log-os absolutorum 23, 197, 203, 1997, 2003, &c.