## Elements of Geometry and Trigonometry |

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Page 57

From A , the point of contact , draw the

From A , the point of contact , draw the

**diameter**AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC ... Page 66

If the given angle were a right angle , the required segment would be a semicircle , described on AB as a

If the given angle were a right angle , the required segment would be a semicircle , described on AB as a

**diameter**. PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common ... Page 90

If from a point A , in the circumference of a circle , two chords AB , AC , be drawn to the extremities of a

If from a point A , in the circumference of a circle , two chords AB , AC , be drawn to the extremities of a

**diameter**BC , the triangle BAC will be right angled at A ( Book III . Prop . B D с XVIII . Cor . 2. ) ... Page 96

In every triangle , the rectangle contained by two sides is equivalent to the rectangle contained by the

In every triangle , the rectangle contained by two sides is equivalent to the rectangle contained by the

**diameter**of the circumscribed circle , and the perpendicular let fall upon the third side . In the triangle ABC , let AD be drawn ... Page 99

For , the perpendicular EG , let fall from a point in the circumference upon the

For , the perpendicular EG , let fall from a point in the circumference upon the

**diameter**, is a mean proportional between DE EF , the two segments of the**diameter**( Prop . XXIII . Co. ) ; and these segments are equal to the given lines ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole