Harriot, Thomas - Mss. 6785

17387

[Commentary:

On this page, Harriot works on Propositions 12 and 13 from Effectionum geometricarum canonica recensio (Viète 1593b, Props 12, . Proposition 12 is mentioned explicitly at the top of the page. The work continues with Proposition 13 below the dividing line.
Propositio XII.
Data media trium proportionalium et differentia extremarum, invenire
Given three proportionals and the difference of the extremes, to find the
Propositio XII.
Data media trium proportionalium & adgregato extremarum, invenire
Given three proportionals and the sum of the extremes, to find the
In both of these propositions, Viète showed how the standard construction for three proportionals can lead to the given equation. Harriot works the other way round: beginning from an equation, he gives a construction that represents the same relationship geometrically. This is what he means by 'effectio æquationis' or 'the construction of an ]

In Effectiones Geometricas. prop. 12 ex 9 et
[Translation: From Effectiones Geometricas, Proposition XII, from pages 9 and ]

Data media trium proportionalium et differentia extremarum: invenire

[Translation: Given the mean of three proportionals and thd difference of the extremes, find the ]

Data.
Media.
Differentia.

[Translation: Given.
Mean.
Difference.
]

Data Media trium proportionalium et
aggregato extremarum: invenire
[Translation: Given the mean of three proportionals and the sum of the extremes, find the ]

Data.
Media.
Adgreg.

[Translation: Given.
Mean.
Sum.
]

Methodus ad exhibenda quæsita
in numeris.
Dimidium
Subtrahe

\sqrt{36}

id est

D F

vel

A I

. pro

G I

. Adde pro

I H

Multiplica

I H

per

G I

. et erit
Hoc est.
Cuius radix.
Ergo

A C

6 \frac{1}{2}

vel

\frac{13}{2}

\frac{5}{2}

I D

est

F C

4

. prima proportionalis.

\frac{13}{2}

plus

\frac{5}{2}

est

B F

9

. tertia
[Translation: A method of showing the sought quantities in numbers.
Halve.
Subtract

\sqrt{36}

, that is

D F

, or

A I

for

G I

.
Add for

I H

Multiply

I H

G I

and it will be
That is
Whose root is
Therefore

A C

(

6 \frac{1}{2}

\frac{13}{2}

) minus

I D

(

\frac{5}{2} I D

) is

F C

, or

4

, the first proportional.

\frac{13}{2}

plus

\frac{5}{2}

B F

, or

9

, the third proportional.

Brevius.
Et est accurate
modus
[Translation: More briefly.
And it is precisely the ancient ]

Poste.
Etsi modus operandi videtur specie quadam differe antiquo
consideranti tamen, et operanti per commpendium; est omnino
[Translation: Postscript.
Although the mode of operation seems in certain respects to differ from the ancient way, nevertheless examined, and carried out more briefly, it is exactly the same.

51 (26)	52 (26v)
53 (27)	54 (27v)
55 (28)	56 (28v)
57 (29)	58 (29v)
59 (30)	60 (30v)

List of thumbnails

Text layer

Text normalization

Search