Pure Mathematics, Volumen11874 |
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Página 108
... exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D. The exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC ...
... exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D. The exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC ...
Página 109
... angle of the triangle ABC , it is greater than the interior and opposite angle ABC ( I. 16 ) . To each of these add ... exterior angle of the triangle BDC , it is greater than the interior and opposite angle BCD ( L. 16 ) . But the ...
... angle of the triangle ABC , it is greater than the interior and opposite angle ABC ( I. 16 ) . To each of these add ... exterior angle of the triangle BDC , it is greater than the interior and opposite angle BCD ( L. 16 ) . But the ...
Página 111
... angle . Let ABC be a triangle , and from the points B , C , the ends of the side BC , let the two straight lines BD ... exterior angle of a triangle is greater than the interior and opposite angle ( I. 16 ) , therefore BDC , the ...
... angle . Let ABC be a triangle , and from the points B , C , the ends of the side BC , let the two straight lines BD ... exterior angle of a triangle is greater than the interior and opposite angle ( I. 16 ) , therefore BDC , the ...
Página 117
... angle BHA is equal to the angle EFD ( I. 4 ) . But the angle EFD is equal to the angle BCA ( Hyp . ) ; Therefore the angle BHA is also equal to the angle BCA = BCA . ( Ax . 1 ) ; That is , the exterior angle BHA of the triangle AHC , is ...
... angle BHA is equal to the angle EFD ( I. 4 ) . But the angle EFD is equal to the angle BCA ( Hyp . ) ; Therefore the angle BHA is also equal to the angle BCA = BCA . ( Ax . 1 ) ; That is , the exterior angle BHA of the triangle AHC , is ...
Página 118
... exterior angle AEF is greater than the interior and opposite angle EFG ( I. 16 ) . But the angle AEF is also equal to EFG ( Hyp . ) , which is impossible ; Therefore AB and CD , being produced , do not meet towards B , D. In like manner ...
... exterior angle AEF is greater than the interior and opposite angle EFG ( I. 16 ) . But the angle AEF is also equal to EFG ( Hyp . ) , which is impossible ; Therefore AB and CD , being produced , do not meet towards B , D. In like manner ...
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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.