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

### Fra bogen

Resultater 1-5 af 29

Side 11

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**sides**are opposite , viz . the angle ACF to the angle ABG , and the angle AFC to ...**BC**is common to the two triangles BFC , CGB ; wherefore these triangles are ...**side**of the base . Therefore the angles at the base , & c . Cor . Hence ... Side 12

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**side**AB shall be equal to the**side**AC . A B -- CONSTRUCTION For , if AB be not equal to AC , one of them is greater ...**BC**is common to both , the two**sides**DB ,**BC**, are equal to the two AC , CB , each to each ; and the angle DBC is ... Side 14

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**side**of the other . A B This case needs no demonstration , for it is evident ...**sides**of the one equal to two**sides**of the other , each to each , and have ...**BC**equal to the base EF . Then the angle BAC shall be equal to the angle EDF ... Side 15

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**BC**upon EF ; then because**BC**is equal to EF , ( hyp . ) therefore the point ...**side**of it , there can be two triangles that have their**sides**which are ...**BC**coincides with the base EF , the**sides**BA , AC , cannot but coincide with the ... Side 16

Euclides Alexander Kennedy Isbister. upon the

Euclides Alexander Kennedy Isbister. upon the

**side**of it opposite to A ...**sides**DA , AF , are equal to the two**sides**EA , AF , each to each ; and the base DF is ...**BC**, CD , each to each ; and the angle ACD is equal to the angle BCD ...### Andre udgaver - Se alle

The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Ingen forhåndsvisning - 2009 |

### Almindelige termer og sætninger

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

### Populære passager

Side 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...

Side 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.

Side 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...

Side 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.

Side 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...

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

Side 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.

Side 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.

Side 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.