Pure mathematics, Volume 11874 |
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Page 92
... 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 ...
... 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 98
... Join FC , GB . PROOF . - Because AF is ( Construction ) , and AB is ( Hyp . ) , equal to AG equal to AC 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 ...
... Join FC , GB . PROOF . - Because AF is ( Construction ) , and AB is ( Hyp . ) , equal to AG equal to AC 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 99
... 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 ACB ...
... 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 ACB ...
Page 100
... 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 ) . ZADC . BDC > BCD . < BDC = Z BCD . BDC = and > 4 BCD . Again ...
... 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 ) . ZADC . BDC > BCD . < BDC = Z BCD . BDC = and > 4 BCD . Again ...
Page 102
... 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 ...
... 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 ...
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amount base called cent centre circle common Const contained decimal denominator describe difference distance divided divisible divisor double draw drawn equal equation evident example expression factor figures Find four fraction give given greater half Hence hour integer interest join less letters logarithm measure meet metres miles Multiply negative obtained opposite parallel parallelogram pass perpendicular places positive PROOF.-Because Q. E. D. Proposition quantity quotient ratio rectangle Reduce remainder respectively result right angles rule segment sides square square root straight line subtraction third touch triangle twice units whole
Popular passages
Page 272 - The angles in the same segment of a circle are equal to one another.
Page 103 - 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 233 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines, and let BC be divided into any...
Page 112 - IF two triangles have two sides of the one equal to two sides of the...
Page 128 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 119 - 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 together equal to two right angles.
Page 113 - ... equal angles in each ; then shall the other sides be equal, each to each ; and also the third angle of the one to the third angle of the other.
Page 273 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Page 281 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 121 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.