Elements of Geometry and Trigonometry |
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Page 59
... divided into two equal parts ; and thus , by successive subdivisions , a given angle , or a given arc may be divided into four equal parts , into eight , into sixteen , and so on . r PROBLEM VI . Through a given point , to draw BOOK III .
... divided into two equal parts ; and thus , by successive subdivisions , a given angle , or a given arc may be divided into four equal parts , into eight , into sixteen , and so on . r PROBLEM VI . Through a given point , to draw BOOK III .
Page 71
... divided into 7 equal parts , AE will contain 4 of those parts : at each point of division erect a perpendicular to the base ; seven partial rect- angles will thus be formed , all equal to each other , because all have the same base and ...
... divided into 7 equal parts , AE will contain 4 of those parts : at each point of division erect a perpendicular to the base ; seven partial rect- angles will thus be formed , all equal to each other , because all have the same base and ...
Page 75
... pressed by EF × HI : it is therefore equal to the altitude of the trapezoid multiplied by the line which connects the middle points of its inclined sides . PROPOSITION VIII . THEOREM . If a line is divided BOOK IV . 113 75.
... pressed by EF × HI : it is therefore equal to the altitude of the trapezoid multiplied by the line which connects the middle points of its inclined sides . PROPOSITION VIII . THEOREM . If a line is divided BOOK IV . 113 75.
Page 76
... 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 . This property is ...
... 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 . This property is ...
Page 86
... divided into triangles , and any triangle into two right angled triangles . Thus the general properties of triangles include , by implica- tion , those of all figures . PROPOSITION XX . THEOREM . Two triangles , which have an angle of ...
... divided into triangles , and any triangle into two right angled triangles . Thus the general properties of triangles include , by implica- tion , those of all figures . PROPOSITION XX . THEOREM . Two triangles , which have an angle of ...
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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