Harriot, Thomas - Mss. 6785

279140

[Commentary:

Harriot refers to Euclid,
If four magnitudes be proportional they will also be proportional alternately.
If magnitudes be proportional componendo, they will also the proportional separando. ]

1.Of three magnitudes in continuall proportion; the summe of the first
& second being given & the summe of the second and third: to find the

By the 17 of the 5th as the first & second hath to the second, so hath the second
& third to the third. Therefour (alterne) by the 16 of the 5th, as the summe
of the first and second hath unto the summe of the second & third,
so hath the second to the third. Then agayne (componendo) by the
same 17 prop. as the aggregate of the two summes hath to the
summe of the second & third, so hath the summe of the second & third
to the third. The third being known the rest are also known, &
therefour the proportion

2. Of three proportionalls in continuall proportion: the difference
betwixt the first & last & the summe of the second & third being given to find
the

It must be understood also which is the least terme & let that for sake of
delivery be recconed the first. Then subtract that first difference
out of the sayd summe of the second & third & then will remayne the
summe of the first & second as is thus proved. Suppose the
three magnitudes unkown be

a b

b c

c d

. from

c

towarde

d

there
is a mgnitude æquall to

a b

which
let be

c e

. Then

e d

wilbe the difference which is given. Which being
subtracted out of

b d

the summe of second & third, leaveth

b e

; which
is æquall to

a c

by the 2 common substrates, the summe of the first & second.
The proposition then is as that

This propostion wrought by algebra the
first being suppose

1 a

is as

191 (96)	192 (96v)
193 (97)	194 (97v)
195 (98)	196 (98v)
197 (99)	198 (99v)
199 (100)	200 (100v)

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