Elements of Geometry |
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Page 50
... divided into two parts AB , BC , the square described upon the whole line AC will contain the square described upon the part AB , plus the square described upon the other part BC , plus twice the rectangle contained by the two parts AB ...
... divided into two parts AB , BC , the square described upon the whole line AC will contain the square described upon the part AB , plus the square described upon the other part BC , plus twice the rectangle contained by the two parts AB ...
Page 51
Adrien Marie Legendre. = The square ACDE is divided into four parts ; the first ABIF is the square described upon AB , since AF was taken equal to AB ; the second IGDH is the square described upon BC ; for , since AC AE , and ABAF , the ...
Adrien Marie Legendre. = The square ACDE is divided into four parts ; the first ABIF is the square described upon AB , since AF was taken equal to AB ; the second IGDH is the square described upon BC ; for , since AC AE , and ABAF , the ...
Page 62
... divided into equal parts at the points F , G , H , the parallel DE would be divided likewise into equal parts at the points I , K , L. Fig . 126 . THEOREM . 213. If , from the right angle A ( fig . 126 ) of a right - angled triangle ...
... divided into equal parts at the points F , G , H , the parallel DE would be divided likewise into equal parts at the points I , K , L. Fig . 126 . THEOREM . 213. If , from the right angle A ( fig . 126 ) of a right - angled triangle ...
Page 72
... divided into five equal parts . For , since CI is parallel to GB , the sides AG , AB , are cut proportionally in C and I ( 196 ) . But AC is a fifth part of AG , therefore AI is a fifth part of AB . 2. Let it be proposed to divide the ...
... divided into five equal parts . For , since CI is parallel to GB , the sides AG , AB , are cut proportionally in C and I ( 196 ) . But AC is a fifth part of AG , therefore AI is a fifth part of AB . 2. Let it be proposed to divide the ...
Page 73
... divided at the point Fin the manner required ; that is , = AB : AF :: AF : FB . For AB , being a perpendicular to ... divided in this manner , it is said to be divided in extreme and mean ratio . Its application will be seen hereafter ...
... divided at the point Fin the manner required ; that is , = AB : AF :: AF : FB . For AB , being a perpendicular to ... divided in this manner , it is said to be divided in extreme and mean ratio . Its application will be seen hereafter ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence