Elements of Geometry |
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Page 105
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 107
... plane , and thus it will be perpendicular 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 , AC ... Planes and Solid Angles . 107.
... plane , and thus it will be perpendicular 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 , AC ... Planes and Solid Angles . 107.
Page 108
... 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 per- pendicular 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 per- pendicular A meets this plane , take three points B , C , D ...
Page 109
... 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 Solid Angles . 109.
... 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 Solid Angles . 109.
Page 111
... 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 . 111.
... 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 . 111.
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence