Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 55
Page 44
... fall on G ; therefore , the chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will also be equal . For , if the radii CD , OG ...
... fall on G ; therefore , the chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will also be equal . For , if the radii CD , OG ...
Page 45
... , this perpendicular is the same as the one let fall from the centre on the same chord , since both of them pass through the centre and middle of the chord . PROPOSITION VII . THEOREM . Through three given points not BOOK III . 45.
... , this perpendicular is the same as the one let fall from the centre on the same chord , since both of them pass through the centre and middle of the chord . PROPOSITION VII . THEOREM . Through three given points not BOOK III . 45.
Page 46
... fall from the same point B , on the same straight line , which is impossible ( Book I. Prop . XIV . ) ; hence DE , FG , will always meet in some point O. And moreover , this point O , since it lies in the perpendicular DE , is equally ...
... fall from the same point B , on the same straight line , which is impossible ( Book I. Prop . XIV . ) ; hence DE , FG , will always meet in some point O. And moreover , this point O , since it lies in the perpendicular DE , is equally ...
Page 47
... fall CF perpendicular to this chord , and CI perpendicu- lar to AH . It is evident that CF is greater than CO , and CO than CI ( Book I. Prop . XV . ) ; therefore , CF is still greater than CI . But CF is equal to CG , because the ...
... fall CF perpendicular to this chord , and CI perpendicu- lar to AH . It is evident that CF is greater than CO , and CO than CI ( Book I. Prop . XV . ) ; therefore , CF is still greater than CI . But CF is equal to CG , because the ...
Page 48
... fall from the centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the circle , and be a secant . PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be ...
... fall from the centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the circle , and be a secant . PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be ...
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