Leibniz-Handschriften zur Mathematik LH 35, 3 B 19, fol. 6r
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: 0.79.
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The machine reads it as
- repenetur in integris
- e
- 4
- a +6ab = 3ab,
- 4
- y = b +6 ab5 - 34b
- et latera
- E
- L
- n- 49) -4
- B8 et per consequem
- cate pro rectis
- Et pro ipsit P, 4,r, habebimus tres formulas pagina praecedente
- signatas 5.
- Alia via sit ly - lx = aa BZ- ly = bb
- lco -lZ = d
- numeri erunt (X, lx.aa, Ex = aa - bb (∞ - aa - bb = de, et fieta (X - 3 aa = 2bb - dd = le
- unde pro seu lx = = lc + 32a + 2bb +d0. quo valore substituto habentur et ly, 1Zeco
- punc Jam residuae differentiae, 2da, otia quinta differentiae erunt
- aa + bb, aa + bb + dd, aa + dd qui ut aequentur Quadhatis Formetur ex
- recstarus
- et reusproce de pF et 1.
- pq et rs triangum 2p9rS, ppgq- rrssi pp9q+r
- trianus. rectanus. 2pgr(, Gp rr -4qs), pp rr +94 et sumaturaltitum
- Communis 2 p4Y pro b,, et duo latera pp, 49 rrB, pprr. 4uss pro duabus
- alus literis d, b, tunc duae differentiae aa + bb, et aatdd erunt quadratie
- sa
- ex natur Mranguer rectanguli. itaque restat tantum differentia aequandi
- pro culus latere ponendo
- quadato aa +bb + dd seu p44 4q. +4 q
- pp44+ ress invenietur S= pr: g, quod cum non sit aptum, sumemus
- es
- e
- 9 + 1
- 444
- S+ p Y 4 4
- y+ priqu et integris eut potentia aequanda quadrato P4 + 204Y +pY+
- 44 44 4
- (,34 p 1(gr’y. + 6ppgqr y +6ppabrryu + 4 pqr1 + +p Br y +4y + qr y
- s
- lui latus si sumas ppa+ ppr + 2p qy + ggrrsy + 2Frryd
- et y+ H seu 5=
- ul
- a
- 6p9 + 3pgor- or
- 64r+39rd - 9)
- quaturati quadratorum quorum sutama
- 604
- atu aju
- 14
- 10110
- 6qr + 34r = qr
- 6bE, 2ab292a b +4a b +64862
- 10510.
- 141
- fiet y =2pbp- 1Y ∞Y
- 692113910 -
- et pro quatuor lateribus P9, Y5, p5, 45, (quatumr
- 641,6+ 34b1r - L10
- 695Y + 34r9 - qur
- a rab L6a b0a b +21 aD 4620
- 10 1614
- 10(10 etI2
- qu
- 44 44 44 44
- ( Hic simul invenire quatuorquadrato
- s quabratos, quorum sum maquadratus
- 1ts2 120
- a +164b4 21 a b 6463-32 a b - 6 a +21ab Hb a b +b
- 20
- 4
- sacert differentiam aa +bb +dd, seu pq eY5+ p5 + 4S
- in integris habebuntur haec: 6gr + 3991-
- quatuor numeriquaesit
- a
- p1
- 10
- nempe sit ph= f +s= g prxt qu. K
- fiat p- f: q se g. r A = R: Y
- L K:q
- ergo g: r = K: 4 sea Y = 9quK. et
- p = tik: 99 = f:g. Ergo sit fa = HK
- unde palet horum quatuor quadrato
- quadralorum latera hic habere aliquam
- dependentiam inter e. Et problema
- sic fieri potuisse invenire quatuor
- qu ub biquodratos quorum duo
- sint c inter se, ut alio duo reliqui
- sunt intur se, hinc et strictius aatem
- possumus invenire quatior biquadrato qui
- sint en continua propessione geome
- trica
- si d
Cite
Leibniz-Handschriften zur Mathematik LH 35, 3 B 19, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068268:0011?run=74