## Elements of geometry, based on Euclid, book i1877 |

### From inside the book

Results 1-5 of 22

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**joining**two of its opposite angles . All other four - sided figures are called trapeziums . Postulates . 1. Let it be granted that a straight line may be drawn from any one point to any other point . 2. That a terminated straight line ... Page 14

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**Join**FC , GB . PROOF . - Because AF is equal to AG ( Construction ) , and AB is equal to AC ( Hyp . ) , Therefore the two sides FA , AC are equal to the two sides GA , AB , each to each ; And they contain the angle FAG , common to the ... Page 15

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**Join**DC . PROOF . Because in the triangles DBC , ACB , DB is equal to AC , and BC is common to both , Therefore the two sides DB , BC are equal to the two sides AC , CB , each to each ; And the angle DBC is equal to the angle АСВ ( Нур ... Page 16

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**Join**CD . PROOF . Because AC is equal to AD ( Hyp . ) , The triangle ADC is an isosceles triangle , and the angle 4 ACD ACD is therefore equal to the angle ADC ( I. 5 ) . LADC . BDC > BCD . < BDC = 4 BCD . < BDC = and > Z BCD . Again ... Page 18

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**Join**DE . Upon DE , on the side remote from A , de- scribe an equilateral triangle DEF ( I. 1 ) .**Join**AF . Then the straight line AF shall bisect the angle BAC . PROOF . - Because AD is equal to AE ( Const . ) , and AF is common to the ...### Other editions - View all

### Common terms and phrases

ABC is equal adjacent angles alternate angles angle ABC angle BAC angle BCD angle contained angle EDF angle EGB angle GHD angles BGH angles CBE angles equal bisect centre cloth Const describe the circle diagonal equal sides equal to BC equal triangles equilateral triangle exterior angle Fcap four right angles GHD Ax given point given rectilineal angle given straight line given triangle gram HENRY EVERS interior and opposite isosceles triangle join less Let ABC LL.D meet opposite angles parallel straight lines parallel to BC parallelogram ABCD perpendicular Post 8vo PROOF PROOF.-Because Q. E. D. Proposition rectilineal figure remaining angle right angles Ax side BC sides are opposite sides equal square described square GB third angle trapezium triangle ABC triangle DEF WILLIAM COLLINS

### Popular passages

Page 23 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Page 33 - 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.

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

Page 15 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall also be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC...

Page 11 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.

Page 37 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Page 41 - ... together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 15 - J which the equal sides are opposite, shall be equal, each to each, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.

Page 55 - IF the square described upon one of 'the sides of a triangle be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Page 24 - If, at a point in a straight line, two other straight lines, on the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.