## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 28

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**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 partly adopted from the Encyclopedia Metropolitana , and will , it is believed ... Page 12

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**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 a theorem , or the solution ... Page 15

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**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 FCD will be a right angle ( Prop . I. Cor . 1. ) ; and since ACE is a straight line ... Page 73

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**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 each of their sides equal to unity , as the diagram exhibits . In ... Page 76

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**become**squares , and the square described on the whole line would be equivalent to four times the square described on half the line ... Scholium . This property is equivalent to the property de- monstrated in algebra , in obtaining the ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex