A School Geometry, Teile 1-4Macmillan and Company, 1908 |
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Seite xi
... THEOREM 20. [ Euc . I. 33. ] The straight lines which join the extremities of two equal and parallel straight lines towards the same parts are themselves equal and parallel . 57 PAGE THEOREM 21. [ Euc . I. 34. ] The CONTENTS . xi.
... THEOREM 20. [ Euc . I. 33. ] The straight lines which join the extremities of two equal and parallel straight lines towards the same parts are themselves equal and parallel . 57 PAGE THEOREM 21. [ Euc . I. 34. ] The CONTENTS . xi.
Seite 2
... curved . A straight line has the same direction from point to point throughout its whole length . A curved line changes its direction continually from point to point . AXIOM . There can be only one straight line joining 2 GEOMETRY .
... curved . A straight line has the same direction from point to point throughout its whole length . A curved line changes its direction continually from point to point . AXIOM . There can be only one straight line joining 2 GEOMETRY .
Seite 17
... joining a vertex to the middle point of the opposite side is called a median . THE COMPARISON OF TWO TRIANGLES . ( 1 ) The three sides and three angles of a triangle are called its six parts . A triangle may also be considered with ...
... joining a vertex to the middle point of the opposite side is called a median . THE COMPARISON OF TWO TRIANGLES . ( 1 ) The three sides and three angles of a triangle are called its six parts . A triangle may also be considered with ...
Seite 22
... Join DC . Then in the △ DBC , ACB , DB = AC , BC is common to both , and the included DBC = the included △ ACB ; DBC the ACB in area , == the part equal to the whole ; which is absurd . .. AB is not unequal to AC ; that is , AB AC ...
... Join DC . Then in the △ DBC , ACB , DB = AC , BC is common to both , and the included DBC = the included △ ACB ; DBC the ACB in area , == the part equal to the whole ; which is absurd . .. AB is not unequal to AC ; that is , AB AC ...
Seite 24
... Join DG . Because ED = EG , ... the EDG = the EGD . Again , because FD = FG , ... the FDG the FGD . = EDF = the whole EGF , Hence the whole that is , the EDF = the △ BAC . Theor . 5 . Then in the A BAC , EDF ; BA = ED , because AC = DF ...
... Join DG . Because ED = EG , ... the EDG = the EGD . Again , because FD = FG , ... the FDG the FGD . = EDF = the whole EGF , Hence the whole that is , the EDF = the △ BAC . Theor . 5 . Then in the A BAC , EDF ; BA = ED , because AC = DF ...
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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.