## Elements of Geometry and Trigonometry |

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Page 30

If from the vertex of any one angle A , diagonals p , AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the polygon will be

If from the vertex of any one angle A , diagonals p , AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the polygon will be

**divided**into five triangles , if it has seven sides ; into six ... Page 33

A B For , draw the diagonal DB ,

A B For , draw the diagonal DB ,

**dividing**the quadrilateral into two triangles . Then , since AB is parallel to DC , the alternate angles ABD , BDC , are equal ( Prop . XX . Cor . 2. ) ; moreover , the side DB is common , and the side ... Page 34

Ratio is the quotient arising from

Ratio is the quotient arising from

**dividing**one quantity by another quantity of the same kind . ... Thus , of two magnitudes , one of them may be considered to be**divided**into some number of equal parts , each of the same kind as the ... Page 35

... equal to a constant quantity

... equal to a constant quantity

**divided**by the other , and their product is constant . PROPOSITION I. THEOREM . When four quantities are in proportion BOOK II . 35. Page 52

... mCn , nCp , & c . , into which ACB is

... mCn , nCp , & c . , into which ACB is

**divided**, being each equal to any of the four partial angles into which DČE is**divided**; each of the partial arcs Am , mn , np , & c . , will be equal to each of the partial arcs Dr , xy , & c .### 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