Elements of Geometry |
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Page 107
Adrien Marie Legendre. PART SECOND . SECTION FIRST . Of Planes and Solid Angles . DEFINITIONS . 313. A STRAIGHT line is perpendicular to a plane , when it is perpendicular to every straight line in the plane which passes through the foot ...
Adrien Marie Legendre. PART SECOND . SECTION FIRST . Of Planes and Solid Angles . DEFINITIONS . 313. A STRAIGHT line is perpendicular to a plane , when it is perpendicular to every straight line in the plane which passes through the foot ...
Page 109
... plane , and thus it will be per- pendicular to the plane MN . Demonstration . Through a point Q , taken at pleasure in PQ , draw the straight line BC in the angle BPC , making BQ = QC ( 242 ) ; join AB , AQ ... Planes and Solid Angles . 109.
... plane , and thus it will be per- pendicular to the plane MN . Demonstration . Through a point Q , taken at pleasure in PQ , draw the straight line BC in the angle BPC , making BQ = QC ( 242 ) ; join AB , AQ ... Planes and Solid Angles . 109.
Page 110
... angles APB , APC , APD ( fig . 184 ) , being right angles , if we suppose the distances PB , PC , PD , equal to each ... plane being given , to find the point P where the perpendicular A meets this plane , take three points B , C , D ...
... angles APB , APC , APD ( fig . 184 ) , being right angles , if we suppose the distances PB , PC , PD , equal to each ... plane being given , to find the point P where the perpendicular A meets this plane , take three points B , C , D ...
Page 111
... plane . The least distance of these lines is the straight line PD , which is at the same time perpendicular to the line AP and to the line BC . The distance PD is the shortest ; because , if we join two ... Planes and Solia Angles . 111.
... plane . The least distance of these lines is the straight line PD , which is at the same time perpendicular to the line AP and to the line BC . The distance PD is the shortest ; because , if we join two ... Planes and Solia Angles . 111.
Page 113
... plane ABC to pass inter- secting the plane MN in AD , the intersection AD will be par- allel to BC ( 340 ) ; but the line AB , perpendicular to the plane MN , is perpendicular to the straight line AD ... Planes and Solid Angles . 113.
... plane ABC to pass inter- secting the plane MN in AD , the intersection AD will be par- allel to BC ( 340 ) ; but the line AB , perpendicular to the plane MN , is perpendicular to the straight line AD ... Planes and Solid Angles . 113.
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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