Elements of Geometry |
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Page v
... for deliberating on each step . After a Book has been read in this way the pupil should review the Book , and should be required to draw the figures free - hand . He should state and prove the propositions orally , using a PREFACE .
... for deliberating on each step . After a Book has been read in this way the pupil should review the Book , and should be required to draw the figures free - hand . He should state and prove the propositions orally , using a PREFACE .
Page 15
... prove LOCB = LACP . ZOCA + Z OCB 2 rt . 4 , $ 34 ( being sup . - adj . ) . LOCA + ZACP 2 rt . 4 , § 34 ( being sup . - adj . ) . .LOCA + LOCB LOCA + ZACP . Ax . 1 . Take away from each of these equals the common ZOC A. Then LOCB LACP ...
... prove LOCB = LACP . ZOCA + Z OCB 2 rt . 4 , $ 34 ( being sup . - adj . ) . LOCA + ZACP 2 rt . 4 , § 34 ( being sup . - adj . ) . .LOCA + LOCB LOCA + ZACP . Ax . 1 . Take away from each of these equals the common ZOC A. Then LOCB LACP ...
Page 17
... prove CO < any other line drawn from C to A B , as CF. Produce CO to E , making O ECO . Draw EF . On A B as an axis , fold over OCF until it comes into the plane of O E F The line OC will take the direction of O E , = ( since LCOF LEOF ...
... prove CO < any other line drawn from C to A B , as CF. Produce CO to E , making O ECO . Draw EF . On A B as an axis , fold over OCF until it comes into the plane of O E F The line OC will take the direction of O E , = ( since LCOF LEOF ...
Page 20
... prove CH > CK . Produce C F to E , making F E = C F. Draw EK and E H. = CHHE , and CK = KE , § 53 ( two oblique lines drawn from the same point in a 1 , cutting off equal dis- tances from the foot of the 1 , are equal ) . But CH + HE ...
... prove CH > CK . Produce C F to E , making F E = C F. Draw EK and E H. = CHHE , and CK = KE , § 53 ( two oblique lines drawn from the same point in a 1 , cutting off equal dis- tances from the foot of the 1 , are equal ) . But CH + HE ...
Page 21
... prove FE = FK . Fold over CFA on CF as an axis , until it comes into the plane of C FB . The line FE will take the direction F K , ( < CFE = CFK , each being a rt . 4 ) . Then the point E must fall upon the point K ; otherwise one of ...
... prove FE = FK . Fold over CFA on CF as an axis , until it comes into the plane of C FB . The line FE will take the direction F K , ( < CFE = CFK , each being a rt . 4 ) . Then the point E must fall upon the point K ; otherwise one of ...
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Common terms and phrases
A B C AABC AACB ABCD adjacent angles alt.-int altitude apothem arc A B bisect centre circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon exterior angles figure given line given point given polygon given straight line greater homologous sides hypotenuse isosceles triangle Let A B Let ABC limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment sides of equal sides of similar similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices