Elements of Descriptive GeometryMacmillan and Company, 1878 - 202 páginas |
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Página v
... prob- lems depend . To begin in that way is , I think , to make a mistake ; for , without a knowledge of first principles , it is impossible to get such a grasp of the subject as will make it the useful and effective instrument which it ...
... prob- lems depend . To begin in that way is , I think , to make a mistake ; for , without a knowledge of first principles , it is impossible to get such a grasp of the subject as will make it the useful and effective instrument which it ...
Página 34
... ( Prob . III . Cor . ) , and therefore equal to it ( Theorem XV . Cor . ) , and conse- quently equal to p'b . Then in the two right - angled triangles PQA , and p'ba ' PA1 = p'a ' and PQ = p'b . Therefore the angle A , PQ = a'p'b = B. But ...
... ( Prob . III . Cor . ) , and therefore equal to it ( Theorem XV . Cor . ) , and conse- quently equal to p'b . Then in the two right - angled triangles PQA , and p'ba ' PA1 = p'a ' and PQ = p'b . Therefore the angle A , PQ = a'p'b = B. But ...
Página 36
... ( Prob . IV . ) , and on bc , as base , describe the triangle ba , c , having the sides ba ,, ca , equal to BA and CA respectively . The angle bac will be the angle required . = Proof . The line bc BC , since BC is horizontal ( Theor . XV ...
... ( Prob . IV . ) , and on bc , as base , describe the triangle ba , c , having the sides ba ,, ca , equal to BA and CA respectively . The angle bac will be the angle required . = Proof . The line bc BC , since BC is horizontal ( Theor . XV ...
Página 40
... ( Prob . II . ) and the traces Q and R of BC . The lines LQ and MR will be the traces of the plane required . Proof . Since the points L and M are in the plane LSM , the whole line LM is in it ( def . 3 ) , and therefore the points A and ...
... ( Prob . II . ) and the traces Q and R of BC . The lines LQ and MR will be the traces of the plane required . Proof . Since the points L and M are in the plane LSM , the whole line LM is in it ( def . 3 ) , and therefore the points A and ...
Página 42
... ( Prob . III . ) and determine N and O the traces of this line . LNSO will be the plane required . Proof . Because the plane LSO contains NO , which is parallel to PQ , therefore the plane is parallel to PQ ( Theor . x . ) . It is obvious ...
... ( Prob . III . ) and determine N and O the traces of this line . LNSO will be the plane required . Proof . Because the plane LSO contains NO , which is parallel to PQ , therefore the plane is parallel to PQ ( Theor . x . ) . It is obvious ...
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Términos y frases comunes
abcd auxiliary planes axes BALFOUR STEWART centre common section cone of revolution conical surface Construction contain a given contains the line Crown 8vo curve of intersection describes a circle determine the traces diameter dihedral angles distance draw a line draw a tangent Draw the projections drawn edge ELEMENTARY TREATISE ellipse equal faces Fcap figure find the point find the projections find the traces given line given point given spheres ground line horizontal plane horizontal projection horizontal trace hyperboloid inclined at 45 limiting planes meridian numerous Illustrations Owens College P. G. TAIT pendicular perpendicular plane containing plane LMN plane of projection plane parallel plane required point of intersection position Prob PROBLEM Professor Proof rabatment radius required to find respectively revolving right angles ruled surface straight line surface of revolution tangent plane Theor THEOREM tion trihedral vertex vertical plane vertical projection vertical trace
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