Elementary Geometry ... |
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Página 5
... shew him part at least of the use of it . What is Geometry ? What is the object of the science ? It is not measurement , because that may be done directly . If I want to find the height of a tower , I may go to the top , and let a ...
... shew him part at least of the use of it . What is Geometry ? What is the object of the science ? It is not measurement , because that may be done directly . If I want to find the height of a tower , I may go to the top , and let a ...
Página 17
... Shew that its magnitude does not depend on the length of the arms . 8. What is meant by saying that two points determine a straight line ? 9. What are adjacent angles ; supplementary angles ; reflex angles ? Shew how to find the sum and ...
... Shew that its magnitude does not depend on the length of the arms . 8. What is meant by saying that two points determine a straight line ? 9. What are adjacent angles ; supplementary angles ; reflex angles ? Shew how to find the sum and ...
Página 37
... shew that AO is the bisector of the angle BAC . Let perpendiculars OP , OQ , OR be drawn to the three sides BC , CA , AB . Proof . In the triangles OQC , OPC we have OQC = OPC , ( Constr . ) ) OCQ = OCP , OC common . ( Hyp . ) Therefore ...
... shew that AO is the bisector of the angle BAC . Let perpendiculars OP , OQ , OR be drawn to the three sides BC , CA , AB . Proof . In the triangles OQC , OPC we have OQC = OPC , ( Constr . ) ) OCQ = OCP , OC common . ( Hyp . ) Therefore ...
Página 38
... shew that AB makes equal angles with OA and ов . 2. If the bisectors of the equal angles B , C of an isosceles triangle meet in O , shew that OBC is also an isosceles triangle . 3. The line drawn to bisect the vertical angle of an ...
... shew that AB makes equal angles with OA and ов . 2. If the bisectors of the equal angles B , C of an isosceles triangle meet in O , shew that OBC is also an isosceles triangle . 3. The line drawn to bisect the vertical angle of an ...
Página 41
... Shew how Theorem 12 depends ultimately on the Axioms . 18. Which Theorem in this Section proves that as you increase the angle between the legs of a pair of compasses you also increase the distance between their points ? 19. Shew the ...
... Shew how Theorem 12 depends ultimately on the Axioms . 18. Which Theorem in this Section proves that as you increase the angle between the legs of a pair of compasses you also increase the distance between their points ? 19. Shew the ...
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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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