A School Geometry, Teile 1-4Macmillan and Company, 1908 |
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Seite 1
... proof . These self - evident truths are called Axioms . For instance : Things which are equal to the same thing are ... required . H.S.G. A DEFINITIONS AND FIRST PRINCIPLES . Every beginner knows in a PART I Axioms Definitions Postulates.
... proof . These self - evident truths are called Axioms . For instance : Things which are equal to the same thing are ... required . H.S.G. A DEFINITIONS AND FIRST PRINCIPLES . Every beginner knows in a PART I Axioms Definitions Postulates.
Seite 8
... required to effect the purpose of a problem , or to prove the truth of a theorem . ( iv ) The Proof shews that the object proposed in a problem has been accomplished , or that the property stated in a theorem is true . 4. The letters ...
... required to effect the purpose of a problem , or to prove the truth of a theorem . ( iv ) The Proof shews that the object proposed in a problem has been accomplished , or that the property stated in a theorem is true . 4. The letters ...
Seite 9
... requires no further proof . 6. The following symbols and abbreviations are used in the text of this book . In Part I. .. for therefore , L = is , or are , equal to , Δ " " for angle , triangle . After Part I. pt . for point , perp . for ...
... requires no further proof . 6. The following symbols and abbreviations are used in the text of this book . In Part I. .. for therefore , L = is , or are , equal to , Δ " " for angle , triangle . After Part I. pt . for point , perp . for ...
Seite 10
... required to prove that the LAOC , COB are together equal to two right angles . Suppose OD is at right angles to BA , Proof . Then the AOC , COB together = the three AOC , COD , DOB . Also the AOD , DOB together == - the three = AOC ...
... required to prove that the LAOC , COB are together equal to two right angles . Suppose OD is at right angles to BA , Proof . Then the AOC , COB together = the three AOC , COD , DOB . Also the AOD , DOB together == - the three = AOC ...
Seite 12
... required to prove that OB and OA are in the same straight line . Produce AO beyond O to any point X : it will be shewn that OX and OB are the same line . Proof . Since by construction AOX is a straight line , .. the COX is the ...
... required to prove that OB and OA are in the same straight line . Produce AO beyond O to any point X : it will be shewn that OX and OB are the same line . Proof . Since by construction AOX is a straight line , .. the COX is the ...
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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.