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Page 12
... angle to angle . Perimeter . Teρl μeтρéw , to measure round . Triangle . Tres , angulus , with three angles ... ABC , PRS be right angles ; it is required to prove that ABC is equal to PRS . Proof . If the point B were placed on the ...
... angle to angle . Perimeter . Teρl μeтρéw , to measure round . Triangle . Tres , angulus , with three angles ... ABC , PRS be right angles ; it is required to prove that ABC is equal to PRS . Proof . If the point B were placed on the ...
Page 13
... angle DBC coincides with , and is equal to , the angle QRS . ( Ax . 1. ) But by Def . 14 , the angle ABC is half the angle DBC ; and the angle PRS is half the angle QRS ; and the halves of equals are equal ; therefore the right angle ABC ...
... angle DBC coincides with , and is equal to , the angle QRS . ( Ax . 1. ) But by Def . 14 , the angle ABC is half the angle DBC ; and the angle PRS is half the angle QRS ; and the halves of equals are equal ; therefore the right angle ABC ...
Page 14
... angles ; A it is required to prove that AB , BC are in one straight line . Proof . Because DBA and DBC are together equal to two right angles ; ( Hyp . ) and DBA and DBC , from the figure , make up the angle ABC ; therefore ABC is an angle ...
... angles ; A it is required to prove that AB , BC are in one straight line . Proof . Because DBA and DBC are together equal to two right angles ; ( Hyp . ) and DBA and DBC , from the figure , make up the angle ABC ; therefore ABC is an angle ...
Page 19
... angle BAC = the included angle EDF ; it is required to prove that the triangles are equal in all respects , viz . the base BC equal to the base EF , and the angle B to the angle E , and the angle C to the angle F , and the area ABC to ...
... angle BAC = the included angle EDF ; it is required to prove that the triangles are equal in all respects , viz . the base BC equal to the base EF , and the angle B to the angle E , and the angle C to the angle F , and the area ABC to ...
Page 20
James Maurice Wilson. THEOREM 6 . The angles at the base of an isosceles triangle are equal to one another * . Part . En . Let ABC be an isosceles triangle , having the side AB equal to the side AC ; it is required to prove that the angle ...
James Maurice Wilson. THEOREM 6 . The angles at the base of an isosceles triangle are equal to one another * . Part . En . Let ABC be an isosceles triangle , having the side AB equal to the side AC ; it is required to prove that the angle ...
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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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