## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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Page 397

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**given in species**. Let the sides AB , BC about the acute angle ABC of the tri- angle ABC , which has a right angle at A , have a given ratio to one another ; the triangle ABC is**given in species**. E D F C Take a straight line DE given ... Page 398

... given , and if the sides about another angle have a given ratio to one another ; the triangle is

... given , and if the sides about another angle have a given ratio to one another ; the triangle is

**given in species**. Let the triangle ABC have one of its angles ABC a given . but not a right angle , and let the sides BA , AC about ... Page 399

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**given in species**, wherefore the triangle ABC is also**given in species**. A Thirdly , let the given ratio be the ratio of a greater to a less , that is , let the side AB adjacent to the given angle be greater than AC ; and , as in the ... Page 400

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**given in species**; there- fore also the triangles ABC , ABL are**given in species**. And from this it is evident , that in this third case there are always two triangles of a different species , to which the things mentioned as given in ... Page 402

... given , and if the sides about another angle , both together , have a given ratio to the third side ; the triangle is

... given , and if the sides about another angle , both together , have a given ratio to the third side ; the triangle is

**given in species**. Let the triangle ABC have one angle ABC given , and let the two sides BA , AC about another angle ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore

### Popular passages

Page 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 81 - The angles in the same segment of a circle are equal to one another.

Page 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Page 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 22 - ANY two angles of a triangle are together less than two right angles.

Page 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Page 24 - Any two sides of a triangle are together greater than the third side.