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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 87r, page id 00068195:0173
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propositio mechanica elegans. Ubi et specimen
haracterum  analogias
nificantium, et quodus doomat
mulliflicationes
si gravia G. H. L. M sint aequiponde,
rantia, ill bina priora excentro B
brachiis. AB. CB. bina posteriora ex
centra E brachiis DE. FE. sintque libra
AC et DF aequales erunt bina gravia
priora simul, ad bina gravia posteriora in ratione com
posita binorum brachiorum posteriorum ad bina
brachia priora. seu G+ H ad L+ M, ut DE. FE ad AB. CB
Nam cum sint omna, quatur gravia aequiponderantia,
erunt peciproce ut brachia. Ergo erunt:
G. HI. L: M:: L: AB: 1: CB:. 1. DE. 1: FE.  itaque erunt
GrH. L + M:: I: AB + I: CB: I: DEF LFE seu :: AB+BC: AB. FB:
: DEtEF. DEOFE seu  (quia AB + BC_:: DE+ EF) CM
S: DEoFE: AB. CB
Idem applicari potest ad
Hyperbolam, et progressionem
Harmonicam hoc mudo.
si pro quatuor brachiis FE
FE, AB, BC, DE substituantur
quatuo abscissae NPNS. NR. NQ. NP.
exNK, posito N esse centrum Hyperbolae et
absissae NI NK esse Asymptotos. ita erunt
quae si sint progressionis Arithmeticae erunt
NS +NP aequ. NR + NQ. prorsus ut FE+ DE
asypploto aequ. AB+ BC. ordinatae autem SY. RX. QV.
Ni patallelae P 7 erunt progressionis harmonicae, seu in
recipioca ratione ipsarum NS. NR. NG. N P. 1)
ergo erunt Sy. RX. ZV. PY respondebunt d
ipsis M, G, H L, et proinde habebimus
hoc theorema: QV+ RX: PY4SY.: NB NSGP. N
QVFRX. PY+ SG :: NP. NS. NO. NR. sibe
s si sint quatuor quantitates progressiones Arithmetico, et totidem
aliae ipsis peciproce propartionales progressionis harmonicae, erit
summa duonum meditrum harmonicarum ad duas farmonicas extremas
in composita ti aeiagsum extremarum antimeticarum adduas alitineticas