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Page 3
... Hence the four associated Theorems ( i ) ( ii ) ( iii ) ( iv ) resolve themselves into two Theorems that are independent of one another , and two others that are always and neces- sarily true if the former are true ; consequently it ...
... Hence the four associated Theorems ( i ) ( ii ) ( iii ) ( iv ) resolve themselves into two Theorems that are independent of one another , and two others that are always and neces- sarily true if the former are true ; consequently it ...
Page 9
... Hence a straight angle is equal to two right angles ; or , a right angle is half a straight angle , and a straight line makes with its continuation at any point an angle of two right angles . Def . 15. A perpendicular to a straight line ...
... Hence a straight angle is equal to two right angles ; or , a right angle is half a straight angle , and a straight line makes with its continuation at any point an angle of two right angles . Def . 15. A perpendicular to a straight line ...
Page 35
... DGF is supplementary to DGE , that is , to ACB , and therefore the angle Fis supplementary to the angle C. Q. E. D. COR . Hence the triangles are equal in all respects— 3-2 SECT . II . ] 35 . TRIANGLES . Part. En. Let ABC, DEF be the ...
... DGF is supplementary to DGE , that is , to ACB , and therefore the angle Fis supplementary to the angle C. Q. E. D. COR . Hence the triangles are equal in all respects— 3-2 SECT . II . ] 35 . TRIANGLES . Part. En. Let ABC, DEF be the ...
Page 36
James Maurice Wilson. COR . Hence the triangles are equal in all respects— ( 1 ) If the two angles given equal are right angles or obtuse angles . For then the remaining angles must be acute , and there- fore cannot be supplementary ...
James Maurice Wilson. COR . Hence the triangles are equal in all respects— ( 1 ) If the two angles given equal are right angles or obtuse angles . For then the remaining angles must be acute , and there- fore cannot be supplementary ...
Page 46
... Hence if two parallel straight lines are intersected by a third straight line , the corresponding angles are equal , and the interior angles on the same side are supplementary ; and conversely . THEOREM 24 . Straight lines which are ...
... Hence if two parallel straight lines are intersected by a third straight line , the corresponding angles are equal , and the interior angles on the same side are supplementary ; and conversely . THEOREM 24 . Straight lines which are ...
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Common terms and phrases
AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
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