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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 657, page id 867984570:0693
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=867984570&page=693
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.80
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

qeni
100
LOL L F C F TO
Fs enim (in Fi8. 2, dc 3))
Parallelosrammum.
Ft (in F18. 4.)
Friangulum.
_c.
AD =- Dd
bx =DBF
-D1
Noca. (Fie 2. 3.)
iA = dD. F dF
=br + b1
=FC + CK
= 29 + ap
bn = cs f Cm
FC-= et F Ct
2Ck =B4 + 8B
15 n 10
_c.
FE propterea, in Prima Perie, Semiltis termini primi, major est quam duorum proxime sequen-
tium: e semiltis hujus Cumma secundi ec terrii, major quam Cumma quatuor sequentium: d
semissis Cummae illorum quatuor, major quam summa lequentium octo: es sic deinceps in intini
cum. Nam = dD == br F bn; sed bn = FC; adeoque = dD = br F F6. _c.
Ec, in Sccunda serie, semiltis termini Secundi, elt minor quam lumma duorum proxime le
quencium: e semissis hujus summx, minor quam summa sequentium quatuor: e Sic deinceps in
intinitum.
Fstque series prima, series terminorum in locis paribus; (viz. 25, 47 6, 8, 10, _c.) Se-
ries secunda, cerminorum in locis imparibus; (vi2. 2, 3, 5, 7, 8, ec.) sequentis seriei, vi2.
F2 2 22 3 324 425 5266n 90 ec. in insinicum, = 1. Cujus quidemr S Bonatu
a pro numero terminorum, pro arbicrio sumprorum; ; - est alrimus,  J est summa
omnium inde a principio hucusque, e summa religuorum ad sinem.
Ouodque Ouadrans primi termini in cerria serie, sic minor quam summa duorum proxime
sequentium; e quadrans hujus tumma, minor quam summa seguentium quatuor; e quadrans
hujus proximae Cumma, minor quam summa sequenrium octo: Sic demonstro.
Flto a aequalis tertio vel postremo numero cujulvis cermini Diritorum in cerria columna; Frit
164 = 48 a f 56a = 24
an: a - 2: X: 4 -2: a - 3 a + Za 16 a - 96 a + 232 a - 288 a + 184 a - 48 a
2 ax: 2a- +: X: 24-2: 8a = 12 a + 4 a
2a -2: x: 2a -3: X: 2a- 4 8a - 360 +52a 245
262 - 48 a f 56a- 24
64a - 3848 + 88041- 900a + 486a - 96a
64 ad - 384 a f 938 at - 7152 a + 736a = 192 a
64 a = 364 a + 880 at = 960 a + 406 a = 16 a
24
a A = B
Fit
ec
_c