A School Geometry, Deler 1-4Macmillan and Company, 1908 |
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Side xvi
... difference of their radii . THEOREM 49. [ Euc . III . 32. ] The angles made by a tangent to a circle with a chord drawn from the point of contact are respectively equal to the angles in the alternate segments of the circle . 178 180 ...
... difference of their radii . THEOREM 49. [ Euc . III . 32. ] The angles made by a tangent to a circle with a chord drawn from the point of contact are respectively equal to the angles in the alternate segments of the circle . 178 180 ...
Side xviii
... difference of the squares on two straight lines is equal to the rectangle contained by their sum and difference . COR . If a straight line is bisected , and also divided ( inter- nally or externally ) into two unequal segments , the ...
... difference of the squares on two straight lines is equal to the rectangle contained by their sum and difference . COR . If a straight line is bisected , and also divided ( inter- nally or externally ) into two unequal segments , the ...
Side 34
... difference of any two sides of a triangle is less than the third side . 9. The sum of the distances of any point from the three angular points of a triangle is greater than half its perimeter . X. 10 . The perimeter of a quadrilateral ...
... difference of any two sides of a triangle is less than the third side . 9. The sum of the distances of any point from the three angular points of a triangle is greater than half its perimeter . X. 10 . The perimeter of a quadrilateral ...
Side 45
... difference is 60 ° : find all the angles . 5. The angles at the base of a triangle are 84 ° and 62 ° ; deduce ( i ) the vertical angle ( ii ) the angle between the bisectors of the base angles . Check your results by construction and ...
... difference is 60 ° : find all the angles . 5. The angles at the base of a triangle are 84 ° and 62 ° ; deduce ( i ) the vertical angle ( ii ) the angle between the bisectors of the base angles . Check your results by construction and ...
Side 106
... difference in Fig . 2 , the ABC is half the rectangle BDEC . Q.E.D. COROLLARY . A triangle is half any parallelogram on the same base and between the same parallels . For the AABC is half the rect . BCED . And the rect . BCED = any parm ...
... difference in Fig . 2 , the ABC is half the rectangle BDEC . Q.E.D. COROLLARY . A triangle is half any parallelogram on the same base and between the same parallels . For the AABC is half the rect . BCED . And the rect . BCED = any parm ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Side 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.
Side 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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.
Side 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.