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

### From inside the book

Results 1-5 of 5

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**EAB**, FDC , because the two EA , AB , are equal to the two FD , DC , each to each ; and the exterior**angle**FDC is equal to the interior**EAB**, ( 1. 29 ) therefore the base EB is equal to the base FC , and the triangle**EAB**equal to the ... Page 74

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**angle EAB**is a right angle ; therefore the rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE ; take away the square of AE , which is common to both ; therefore the remaining rectangle CF , FA ... Page 105

... angle FCE must be equal to the angle ACE , ( ax . 1 ) the less to the greater , which is impossible . wherefore F is ... EAB is equal to the

... angle FCE must be equal to the angle ACE , ( ax . 1 ) the less to the greater , which is impossible . wherefore F is ... EAB is equal to the

**angle EBA**, ( 1. 5 ) therefore the**angles EAB**, EBA are double of the**angle EAB**; but the ... Page 117

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**angle**in a semicircle is a right**angle**; but the**angle**in a segment greater than a semicircle is less than a right ...**EAB**is equal to**EBA**; ( 1.5 ) also , because AE is equal to EC , the**angle**EAC is equal to the**angle**ECA ... Page 140

... angle ABC , BCD , CDA , are severally bisected by the straight lines BD , AC . Hence , because the angle DAB is equal to the angle ABC , ( 1. def . 30 ) and that the

... angle ABC , BCD , CDA , are severally bisected by the straight lines BD , AC . Hence , because the angle DAB is equal to the angle ABC , ( 1. def . 30 ) and that the

**angle EAB**is the half of DAB , and EBA the half of ABC ; the**angle EAB**...### 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.