Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 93
Page 22
... Scholium . At a given point C , in the line AB , it is equally impossible to erect two per- pendiculars to that line . For , if CD , CE , were those two perpendiculars , the angles BCD , BCE , would both be right angles :. hence they ...
... Scholium . At a given point C , in the line AB , it is equally impossible to erect two per- pendiculars to that line . For , if CD , CE , were those two perpendiculars , the angles BCD , BCE , would both be right angles :. hence they ...
Page 25
... therefore , GFB is a right angle ; hence the two lines EC , BD , are perpendicular to the same straight line , and are therefore parallel ( Prop . XVIII . ) , C Scholium . When two parallel straight lines AB , CD BOOK I. 25.
... therefore , GFB is a right angle ; hence the two lines EC , BD , are perpendicular to the same straight line , and are therefore parallel ( Prop . XVIII . ) , C Scholium . When two parallel straight lines AB , CD BOOK I. 25.
Page 26
Adrien Marie Legendre Charles Davies. Scholium . When two parallel straight lines AB , CD , are met by a third line FE , the angles which are formed take particular names . Interior angles on the same side , are those which lie within ...
Adrien Marie Legendre Charles Davies. Scholium . When two parallel straight lines AB , CD , are met by a third line FE , the angles which are formed take particular names . Interior angles on the same side , are those which lie within ...
Page 29
... Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE were produced towards H , the angle DEH would have its ...
... Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE were produced towards H , the angle DEH would have its ...
Page 31
... Scholium . When this proposition is applied to polygons which have re - entrant angles , each re- entrant angle must be regarded as greater than two right angles . But to avoid all ambiguity , we shall henceforth limit our reasoning to ...
... Scholium . When this proposition is applied to polygons which have re - entrant angles , each re- entrant angle must be regarded as greater than two right angles . But to avoid all ambiguity , we shall henceforth limit our reasoning to ...
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex