Pure Mathematics, Volumen11874 |
Dentro del libro
Resultados 1-5 de 56
Página 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 ...
Página 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 ...
Página 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 АСВ ( Нур ...
... 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 ...
Página 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 ) . Z ADC . BDC > BCD . = < BDC = ZBCD . BDC = and > Z 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 ) . Z ADC . BDC > BCD . = < BDC = ZBCD . BDC = and > Z BCD . Again ...
Página 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 ...
Otras ediciones - Ver todas
Términos y frases comunes
a²b a²b² ab² ab³ ABCD algebraical angle ABC angle BAC angle BCD base BC BC is equal bisect brackets cent centim centre circle ABC circumference coefficient common Const cosec cube root decimal figures denominator divided divisor draw equation expression exterior angle factor Find the value fraction given straight line gnomon gram greater Hence integer join kilom less Let ABC logarithm metres miles millig Multiply opposite angles parallel parallelogram perpendicular PROOF.-Because Q. E. D. Proposition quotient ratio rectangle contained remainder right angles segment sides sin² sine square on AC square root subtraction touches the circle triangle ABC twice the rectangle x²y² x³y xy³
Pasajes populares
Página 272 - The angles in the same segment of a circle are equal to one another.
Página 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.
Página 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...
Página 112 - IF two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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.
Página 273 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Página 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.
Página 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.