A School Geometry, Teile 1-4Macmillan and Company, 1908 |
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Seite xiv
... circle at more than two points . COR . 3. A chord of a circle lies wholly within it . THEOREM 32. One circle , and only one , can pass through any three points not in the same straight line . 144 145 . 145 145 146 COR . 1. The size and ...
... circle at more than two points . COR . 3. A chord of a circle lies wholly within it . THEOREM 32. One circle , and only one , can pass through any three points not in the same straight line . 144 145 . 145 145 146 COR . 1. The size and ...
Seite xv
... circle more than two equal straight lines can be drawn to the circumference , that point is the centre of the circle . THEOREM 34. [ Euc . III . 14. ] Equal chords of a circle are equi- distant from the centre . Conversely , chords ...
... circle more than two equal straight lines can be drawn to the circumference , that point is the centre of the circle . THEOREM 34. [ Euc . III . 14. ] Equal chords of a circle are equi- distant from the centre . Conversely , chords ...
Seite xvi
... circle from an external point . 176 COR . The two tangents to a circle from an external point are equal , and subtend equal angles at the centre . 176 THEOREM 48. If two circles touch one another , the centres and the point of contact ...
... circle from an external point . 176 COR . The two tangents to a circle from an external point are equal , and subtend equal angles at the centre . 176 THEOREM 48. If two circles touch one another , the centres and the point of contact ...
Seite xvii
... circle a segment containing a given angle , it is enough to draw a tangent to the circle , and from the point of contact to draw a chord making with the tangent an angle equal to the given angle . Circles in Relation to Rectilineal ...
... circle a segment containing a given angle , it is enough to draw a tangent to the circle , and from the point of contact to draw a chord making with the tangent an angle equal to the given angle . Circles in Relation to Rectilineal ...
Seite xviii
... Circles . THEOREM 57. [ Euc . III . 35. ] If two chords of a circle cut at a point within it , the rectangles contained by their segments are equal . THEOREM 58. [ Euc . III . 36. ] If two chords of a circle , when produced , cut at a ...
... Circles . THEOREM 57. [ Euc . III . 35. ] If two chords of a circle cut at a point within it , the rectangles contained by their segments are equal . THEOREM 58. [ Euc . III . 36. ] If two chords of a circle , when produced , cut at a ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Seite 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.
Seite 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 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.
Seite 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 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.
Seite 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.