Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 3r
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.87.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.
The machine reads it as
- Theor.
- 23) Suttrahenda arcribuntur signis
- mutatis, + in -, et - in +, seu
- f- (a - b) - f- a + b.
- d
- b
- Nam f- (a - b) = (per 20)b
- = (per 18) f - a + b 2. E D.
- Aliter: Sit a - b = e, ajo erse - e - - a+b
- seu f- c = f - a + b. Nam + e - e =
- + a - b - a + b (per 1) Ergo ab aqua-
- libus tollendo aequalia, illinc + e, hinc
- + a = b restabunt (per 12) aqualia
- =e et - a + b 8. Fi. D.
- AP DL ICATIO CALCVLI ADRE5
- ubi de Toto, parte; majore, minore;
- positivo et privatino
- si subtractio vel signum = evanescat,
- (24) Explic. Elesi explicando notas for-
- mula per res ipras, verbi gratia per
- loneas rectas, sibi addem dac vel subtrahendas; ex evants cat tandem subtractio vel signum-
- ita
- tratendes semper destruendo id quod est signo
- = affertum sucib. gr. - b) per aignalis
- molis signo + affertum, (nempe +b); tandem nihil aliud
- remaneat in formula vel
- dis gaequiva-
- lente re, exgr. Linea afertum signo+ : Tunc tota formula repdicitur designare
- minativa seu nihilo minore Hoc eet,
- talem, ut ad ipram, andenda sit ipsius
- moles, quo fiat nihil. Nempe quia veluti Exempli ausa si esset + C +b b
- (per 11) a d a ad das
- a fit0.
- d
- Aolium. Onrpiriantur figura duae, ubi
- in priore progreesus tit per lineam reitam
- et huic in derectum adjeitam rectam in hac formula, pro fta, suct
- fie
- a regressus per puncta dessignatus absiestsormota
- extremo adjertu a in eadem certa
- totali +a fit per pertam , ita in
- 1Fetmut
- recta fia remanet e adeoque est fa-b- te. Hinc patet quando duae quantitates
- =g. significant
- Setolium
- Alc. 19, doem raetam 3, i q maitore ls)
- +(quae quantit
- formula
- et hae litere op s sianisica rent quantitates posi
- tivas, +ta = b, et esset f+ a = e + b
- hae literae omnes forent quantitates positiuae
- resluta explicatae per res nullum in ultima
- resolutione deprehenderetur continere signum
- patet f+a -b significare + e. Nam
- rest
- resolutione smmlcunt remaneret sigsnum f. H
- ta = d, et esset d=f+at
- tunc f+a= d significabit - g. Nam pros
- in formula f+ a ad. substit uendo valorem
- fiet f+a = f- a =g, id est - q
- signis contraris affectae conjunguntur
- semper alterutrum signorum penitus
- posse tolli per explicationem unius quam
- fitatis, quatenus continet alteram quan-
- titatem (vid. 11) Patet etiam
- formula f+a- d fiat nihil, addi debere
- seu esse f+ a
- d + g= C
- quia sta-d=
- jam -9+g =0. vel resolutione resumta faa
- 2
- f+a-
- g. ( Ergo 5
- d Stanse
Cite
Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 3r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0005?run=73