Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 79
Page 43
... circle , or in equal circles , equal arcs are subtended by equal chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to another , in the same Book , the number of the ...
... circle , or in equal circles , equal arcs are subtended by equal chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to another , in the same Book , the number of the ...
Page 44
... circle , or in equal circles , a greater arc is subtended by a greater chord , and conversely , the greater chord subtends the greater arc . Let the arc AH be greater than the arc AD ; then will the chord AH be greater than the chord AD ...
... circle , or in equal circles , a greater arc is subtended by a greater chord , and conversely , the greater chord subtends the greater arc . Let the arc AH be greater than the arc AD ; then will the chord AH be greater than the chord AD ...
Page 45
... circle , and through the middle of the arc subtended by that chord . For , 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 ...
... circle , and through the middle of the arc subtended by that chord . For , 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 ...
Page 47
... ) ; hence the D point E is without the circle ; therefore , BD has no point but A common to it and the circumference ; consequently BD is a tangent ( Def . 8. ) . Scholium . At a given point A , only one BOOK III . 47.
... ) ; hence the D point E is without the circle ; therefore , BD has no point but A common to it and the circumference ; consequently BD is a tangent ( Def . 8. ) . Scholium . At a given point A , only one BOOK III . 47.
Page 48
... circle , and be a secant . PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There ... circles cut each 48 GEOMETRY .
... circle , and be a secant . PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There ... circles cut each 48 GEOMETRY .
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