A School Geometry, Parts 1-4Macmillan and Company, 1908 |
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Page v
... Parallels ; Use of Set Squares ; The Construction of Triangles and Quadrilaterals . These problems should be ... parallel courses , intended to be studied pari passu . This arrangement is made possible by the use , now generally ...
... Parallels ; Use of Set Squares ; The Construction of Triangles and Quadrilaterals . These problems should be ... parallel courses , intended to be studied pari passu . This arrangement is made possible by the use , now generally ...
Page x
... Parallels . PLAYFAIR'S AXIOM THEOREM 13. [ Euc . I. 27 and 28. ] If a straight line cuts two other straight lines so as to make ( i ) the alternate angles 33 335 equal , or ( ii ) an exterior angle equal X CONTENTS .
... Parallels . PLAYFAIR'S AXIOM THEOREM 13. [ Euc . I. 27 and 28. ] If a straight line cuts two other straight lines so as to make ( i ) the alternate angles 33 335 equal , or ( ii ) an exterior angle equal X CONTENTS .
Page xi
... PARALLELS ILLUSTRATED BY ROTATION . PAGE 36 38 HYPOTHETICAL CON- STRUCTION 39 THEOREM 15. [ Euc . I. 30. ] Straight lines which are parallel to the same straight line are parallel to one another . 40 Triangles continued . THEOREM 16 ...
... PARALLELS ILLUSTRATED BY ROTATION . PAGE 36 38 HYPOTHETICAL CON- STRUCTION 39 THEOREM 15. [ Euc . I. 30. ] Straight lines which are parallel to the same straight line are parallel to one another . 40 Triangles continued . THEOREM 16 ...
Page xii
... parallel straight lines , and the intercepts made by them on any transversal are equal , then the corresponding intercepts on any other transversal are also equal . COR . In a triangle ABC , if a set of lines Pp , Qq , Rr , ... , drawn ...
... parallel straight lines , and the intercepts made by them on any transversal are equal , then the corresponding intercepts on any other transversal are also equal . COR . In a triangle ABC , if a set of lines Pp , Qq , Rr , ... , drawn ...
Page xiii
... parallels are equal in area . 104 AREA OF A PARALLELOGRAM - 105 THEOREM 25. AREA OF A TRIANGLE . 106 THEOREM 26. [ Euc . I. 37. ] Triangles on the same base and between the same parallels ( hence , of the same altitude ) are equal in ...
... parallels are equal in area . 104 AREA OF A PARALLELOGRAM - 105 THEOREM 25. AREA OF A TRIANGLE . 106 THEOREM 26. [ Euc . I. 37. ] Triangles on the same base and between the same parallels ( hence , of the same altitude ) are equal in ...
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Common terms and phrases
AB² adjacent angles altitude angle equal base BC bisector bisects circle of radius circle whose centre circles which touch circum-circle circumference circumscribed coincide common tangents concyclic Construct a triangle diagonals diagram diameter distance divided draw a circle equal in area equidistant escribed circles Euclid exterior angles Find the area find the locus given angle given circle given point given straight line given triangle greater Hence hypotenuse inches inscribed isosceles triangle length Let ABC meet metres middle point millimetre nine-points circle opposite sides orthocentre par¹ parallelogram pedal triangle perp PROBLEM produced Proof radii rect rectangle rectangle contained rectilineal figure required to prove respectively rhombus right angles right-angled triangle segment shew shewn straight line drawn tangent Theor Theorem trapezium triangle ABC triangles are equal vertex vertical angle
Popular passages
Page xi - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Page 44 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 12 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 122 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page x - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 65 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.