Elements of Geometry and Trigonometry |
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Page 10
... produced . 13. A plane figure is a plane terminated on all sides by lines . B B 10 C A D If the lines are straight , the space they enclose is called a rectilineal figure , or polygon , and the lines themselves , taken together , form ...
... produced . 13. A plane figure is a plane terminated on all sides by lines . B B 10 C A D If the lines are straight , the space they enclose is called a rectilineal figure , or polygon , and the lines themselves , taken together , form ...
Page 14
... the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Ax . 11. ) . Sup- E A B D pose , however , that on being produced , these 4 GEOMETRY .
... the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Ax . 11. ) . Sup- E A B D pose , however , that on being produced , these 4 GEOMETRY .
Page 15
... produced ; hence they form one and the same straight line . PROPOSITION III . THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two ...
... produced ; hence they form one and the same straight line . PROPOSITION III . THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two ...
Page 18
... produced till it meets the side AC in D : then the line OC is shorter than OD + DCB ( Prop . VII . ) : add BO to each , and we have BO + OC < BO + OD + DC ( Ax . 4. ) , or BO + OC < BD + DC . Again , BD BA + AD : add DC to each , and we ...
... produced till it meets the side AC in D : then the line OC is shorter than OD + DCB ( Prop . VII . ) : add BO to each , and we have BO + OC < BO + OD + DC ( Ax . 4. ) , or BO + OC < BD + DC . Again , BD BA + AD : add DC to each , and we ...
Page 22
... Produce either of them , as AB , till BF is equal to AB , and De draw FC . Then , the two triangles CAB , CBF , will be equal : for , the angles CBA , and CBF are right angles , the side CB is common , and the side AB equal to BF , by ...
... Produce either of them , as AB , till BF is equal to AB , and De draw FC . Then , the two triangles CAB , CBF , will be equal : for , the angles CBA , and CBF are right angles , the side CB is common , and the side AB equal to BF , by ...
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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