## Elements of Geometry and Trigonometry |

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Page 4

It is proved in the corollaries that a polygon of an infinite number of sides

It is proved in the corollaries that a polygon of an infinite number of sides

**becomes**a circle , and this principle is made the basis of several important de- monstrations in Book VIII . Book II . , on Ratios and Proportions , has been ... Page 12

A theorem is a truth , which

A theorem is a truth , which

**becomes**evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of ... Page 15

pose , however , that on being produced , these lines begin to separate at C , the one

pose , however , that on being produced , these lines begin to separate at C , the one

**becoming**CD , the other CE . From the point C draw the line CF , making with AC the right angle ACF . Now , since ACD is a straight line , the angle ... Page 73

In this case the measurement which we have regarded merely as relative ,

In this case the measurement which we have regarded merely as relative ,

**becomes**absolute : the number 30 , for instance , by which the rectangle A was measured , now represents 30 superficial units , or 30 of those squares , which have ... Page 76

If the line AC were divided into two equal parts , the two rectangles , EI , IC , would

If the line AC were divided into two equal parts , the two rectangles , EI , IC , would

**become**squares , and the square described on the whole line would be equivalent to four times the square described on half the line . Scholium .### 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