## The thirteen books of Euclid's Elements. The works of Archimedes, including The method. Introduction to arithmetic |

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Page 166

Proposition 20 If one mean proportional number fall between two numbers, the

numbers will be

fall between the two numbers A, B; I say that A, B are

D ...

Proposition 20 If one mean proportional number fall between two numbers, the

numbers will be

**similar plane numbers**. For let one mean proportional number Cfall between the two numbers A, B; I say that A, B are

**similar plane numbers**. LetD ...

Page 171

BOOK NINE Proposition 1 // two

another make some number, the product will be square. Let A, B be two

let A by ...

BOOK NINE Proposition 1 // two

**similar plane numbers**by multiplying oneanother make some number, the product will be square. Let A, B be two

**similar****plane numbers**, and let A by multiplying B make C ; I say that C is square. B Forlet A by ...

Page 198

It has been proved in the arithmetical books that

one another the ratio which a square number has to a square number, [vm. 26]

and that, if two numbers have to one another the ratio which a square number

has ...

It has been proved in the arithmetical books that

**similar plane numbers**have toone another the ratio which a square number has to a square number, [vm. 26]

and that, if two numbers have to one another the ratio which a square number

has ...

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### Common terms and phrases

AC is equal angle ABC angle BAC apotome axis base binomial straight line bisected centre of gravity circle ABCD circumference circumscribed commensurable in length commensurable in square cone continued proportion cube cylinder diameter double equal angles equiangular equilateral equimultiples figure fluid frustum gnomon height incommensurable inscribed joined less let the square magnitudes mean proportional medial area medial straight line multiplying parabola paraboloid parallelogram pentagon perpendicular plane of reference polygon prime prism produced Prop Proposition 13 proved pyramid q. e. d. Proposition radius rational straight line rectangle AC rectangle contained remaining angle right angles side similar Similarly sphere spheroid square number squares on AC straight lines commensurable superparticular surface tangent triangle ABC twice the rectangle vertex whole