## The school Euclid: comprising the first four books, by A.K. Isbister1862 |

### From inside the book

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**parts**in C. Then the**rectangle*****contained**by AB and BC , together with the**rectangle contained**by AB and AC ,**shall be equal to the square**of AB . A C B D F E CONSTRUCTION Upon AB describe the**square**ADEB , (**1**. 46 ) and through C draw ... Page 66

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**rectangle**AL is**equal**to CH , (**1**. 36 ) but CH is**equal**to HF ; (**1**. 43 ) therefore also AL is**equal**to HF ; to each of these add CM ; therefore the**whole**AM is**equal**to the gnomon CMG . But AM is the**rectangle contained**...**square**of CB ; ... Page 68

Euclides Alexander Kennedy Isbister.

Euclides Alexander Kennedy Isbister.

**parts**, together with the**square of the other part**, is**equal to the square**of the straight line which is made up of the**whole**and that**part**. - ( References Prop .**1**. 3 , 31 , 34 , 36 , 43 , 46 ; п ... Page 69

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**equal**to**one another**, and so are quadruple of**one**of them , AG . And it was ...**rectangle contained**by AB , BC , for BK is**equal**to BC , therefore four ...**square**of AC ; ( 11.4 , Cor . ) therefore four times the**rectangle**AB , BC ... Page 73

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**equal**to the**side**FE . And because EC is**equal**to CA , the**square**of EC is ...**parts**, so that the**rectangle**con- tained by the**whole and one of the parts shall be equal to the square of the other part**...**contained by the whole and one of the**...### Other editions - View all

The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister No preview available - 2009 |

### Common terms and phrases

AB is equal adjacent angles alternate angles angle ABC angle AGH angle BAC angle BCD angle EAB angle EDF angle equal angles CBA base BC BC is equal circle ABC constr DEMONSTRATION describe the circle diameter double equal angles equal straight lines equal to BC equilateral and equiangular exterior angle given circle given rectilineal angle given straight line gnomon greater inscribed interior and opposite less Let ABC Let the straight opposite angles parallel to CD parallelogram pentagon perpendicular Q. E. D. PROP rectangle AE rectangle contained rectilineal figure References Prop References-Prop remaining angle required to describe right angles segment semicircle side BC square of AC straight line AB straight line AC THEOREM touches the circle triangle ABC triangle DEF twice the rectangle

### Popular passages

Page 141 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 35 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Page 71 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Page 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Page 61 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...

Page 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Page 27 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.

Page 77 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.

Page 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.