## Elements of Geometry and Trigonometry |

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Page 11

The side

The side

**opposite**the right angle is called the hypothenuse . Thus , in the triangle ABC , right - angled at A , the side BC is the hypothenuse . B ЈА 17. Among the quadrilaterals , we distinguish : The square , which has its sides ... Page 15

PROPOSITION IV . THEOREM . When two straight lines intersect each other , the

PROPOSITION IV . THEOREM . When two straight lines intersect each other , the

**opposite**or ver tical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting BOOK I. 15. Page 16

Take away from both , the com- mon angle ACE , there remains the angle ACD , equal to its

Take away from both , the com- mon angle ACE , there remains the angle ACD , equal to its

**opposite**or vertical angle ECB ( Ax . 3. ) . Scholium . The four angles formed about a point by two straight lines , which intersect each other ... Page 20

... the angles

... the angles

**opposite**the equal sides are equal . Let the side BA be equal to the side AC ; then will the angle C be equal to the angle B. A For , join the vertex A , and D the middle point of the base BC . Page 21

First , Let the angle C be greater than the angle B ; then will the side AB ,

First , Let the angle C be greater than the angle B ; then will the side AB ,

**opposite**C , be greater than AC ,**opposite**B. For , make the angle BCD = B . Then , in the triangle CDB , we shall have CD BD ( Prop . XII . ) .### 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 construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole