Elements of Geometry |
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Page 12
... half of AF is less than AC half of AC + CF ; that is , the perpendicular is less than any one of the oblique lines . - 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right angle ABE ABC , the triangle ...
... half of AF is less than AC half of AC + CF ; that is , the perpendicular is less than any one of the oblique lines . - 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right angle ABE ABC , the triangle ...
Page 18
... half the angle GFN , or one fourth of the angle GFM . = We are able , therefore , in this manner , to take successively the half , the fourth , the eighth , & c . , of the angle GFM , and the lines which form these divisions meet the ...
... half the angle GFN , or one fourth of the angle GFM . = We are able , therefore , in this manner , to take successively the half , the fourth , the eighth , & c . , of the angle GFM , and the lines which form these divisions meet the ...
Page 26
... half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and ...
... half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and ...
Page 29
... half of AB , is equal to the side DG , the half of DE ; the triangles , then , are equal ( 56 ) , and consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from ...
... half of AB , is equal to the side DG , the half of DE ; the triangles , then , are equal ( 56 ) , and consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from ...
Page 35
... half of the arc BD comprehended between its sides . = Demonstration . Let us suppose , in the first place , that the ... half of BE . For a similar reason , the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD ...
... half of the arc BD comprehended between its sides . = Demonstration . Let us suppose , in the first place , that the ... half of BE . For a similar reason , the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD ...
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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