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# Title: [Quo Continentur Claudii Ptolemaei, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunae, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Graece & Latine Edita, cum Notis ; Accedunt Epistolae nonnullae, rem Mathematicam spectantes; Et Opuscula quaedam Miscellanea] Quo Continentur Claudii Ptolemæi, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunæ, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Græce & Latine Edita, cum Notis ; Accedunt Epistolæ nonnullæ, rem Mathematicam spectantes; Et Opuscula quædam Miscellanea (shelfmark Leibn. Marg. 100:3)
# Folio 630, page id 867984570:0666
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.86
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PISTOL A R V N
Sc intelligatur; Sit (Fis. T.) AOCDA. Fa, ductis rectis BD parallelis, resolri potest im
Traperia 1B2D, 2B3D, erc. Sed, ductis rectis cote LB etM AI  L
sula E. TD2D, E. 2D 3D, ec.
Si jam alia SIE CUErA A IF EF ZF, cujus Traperia IB2F, 2BZF, tint. Triangulis F +D2D
EED 3D, ordinc respondencibus aequalia, coca tigura A P. 3D 2D +D A, cori FixurX A LF 2F 3F
3B A erit aequaliS.
Ouineriam Fraperia Praperiis conterendo, tieri potest ne 1N2P, vel quod eodem redir
Rectangulum INZNY2P, sit aequale Traperio relpondenti 1B2B, lire Rectansulo IB2B2D
camerli recta THIiP non lic aequalis recta IBID, modo sic IN2N ad IB2B ut IBLD ad
TNTTP; quod intinitis modis fieri porelt.
Ouae omnia calia Cune ur cuiris ltacim ordine progredienti, ipsa natura duce, in mentem re-
niane; contineantque Indirilibilium Mechodum generalistime conceptam, nec (quod sciam )
hactenus latis univexsalirer explicatam. Non eancum enim Parallelae e Convergentes, led et
alix quaecunque cerra lege duetaxe, rectaxe vel curra, adhiberi postune ad relolurionem. Ouanta
aurem ec quam abstrula hinc duei pollint, judicabir qui mechodi univerlalitarem animo exit
complexus. Cercum enim elt omnes Guadraturas hactenus notas, absolutas vel hypotheticas,
nonnili exioua ejus (pecimina este.
Sed nunc quidem suttecerit applicationem ostendere ad id de quo asitur; Series scilicet Infi-
nitas, ee modum Franstormandi tiguram datam in aliam xequipollencem racionalem, Mercatoris
mechodo tractandam.
AOCA sic Onadrans Circuli: Racius AO = r: AbScisTa A 1B = x: Ordinata LB+D = y.
Aguatio pro Circulo 2r X = v = y. Ducarur recta AID: producaurque donec ipli QC.
etiam PrOuCA OCCUTAE II YH: Et QIN VOCETUE B. EL CriE A LB seu N =
22
+ _: F.F
1BID Eire y = , f ~. Eodem modo, ducta A2DZH; s Q2N = 2 - B (potita Scilicet
INZN = B) erit A2B = , f v - 23B. f Bi et A2B = A 1B, sive recta 1B2B, exic
2r.
p + 8 = 2. 2B + B r + 25. Sire, polica B intinice parva, (post destructiones et divitio.
413~B
nes,) eric IB2B = - 
=. Habita ergo recta rBFD, e recta 2B2B, habebitur va.
lor Rectanguli 1DFBZB, mulciplicatis eorum valoribus in se invicens; habebitur inquam
8r3 Z ZB
(3), 2 7. -2 Deo valore Rectanguli AD LB2B.
Six jam CUEVX EP ZP 3P _C. nacura pro arbicrio allumpra calis, ut Ordinata ejus +ND XP
Cex daca abscilta Q FN sivc 2) Sic;
Gulum EP AN ZVI, etiam 8r3 22
2
(3) 33 f 25. deo, quoniam LNZN = B, erie rectan.
Ac proinde aequale Rectangnto FD +B2B, e spacium
APLN ZN SPZP EP aequale spacio Circulari respondenti rD +B3B, DZDID. EAI autem qua-
libet Ordinaca NP rationalis, ex dara abseicta ON; quia, posita aN = 2, Ordinata NP est
3r3
8 r3 22
(3) n f 5 Evc p = 3r ~ + 3r. 25 f 25. Ergo ipsa per Intinicam Seriem Incexrorum
exprimi