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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 17
# Folio 10r, page id 00068014:0019
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De summa factionum quarum numergcs constans, nominatoes, Numeri polygoni
Ex Goselino de arte magna sive tgebra lib. 1. cap. H.
Dato latere restigandi polygoni ratio generalis ac facilis:
Anferemus 2 ex numero angulorum; auferemus et monadem a labe
residuos multiplicabimus invicem; facto addemus 2; summu ducta
in lateris semissem, dabit polygonum quae situm
e
v. g. vestigemus. Alum a latere 6 quia triangulum tres habet
anguloe, subductis 2 restat 1, ex 6 aufer 1. restat 5. sjam
1
5 adde 2 fit 7
Triangularis numeres quaesitus
Ego id analytice ita enuntio:
si Numerus angulorum sit b.
latus sit y. Erit polygonum
- 2a Y 1+ 4 aV
s. 10c
C ba..
b- 2, 0 y - 1,, +  y 3
si esset Cy rely + el - βC
iniri poterit summa; fractionum
ab ipsis denominatarum, ut
alibi ame inventum est
sunt autem e. d. B. datae; jam
termini conferantur, fier:
=2a + b,, 2e, et 0p - 2a +b
multi plia per E 3, fiet 21.
L eac HelBC2. Et in polygono peo ypone L XA21257+
jam ut termini ubique conferri possint
scubatur: 2C 92
et jam ordinando: a
e F
2a +b
-2a72 - 4faZ- 2af conferantur ter minitem
l - 4f a + bf + 4a - ba
minis.
+b. + bf. 1b r
44a.. +44)
-ba.. baf
1- 2af + bf + 4a f - baf + 2B5. Quibus valoribus inter se qunctis habebitur
2 er 2a + b 
valor ipsius f. eademue methioit paritertl. Quibus obtentis poterit invencri
fractionum omnium a Polygonis denominatarum, numerato rem con-
stantem habentium summa. In Triungulo ipsa f necessaria
non esst
+ 3