A School Geometry, Teile 1-4Macmillan and Company, 1908 |
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Seite xviii
... COROLLARIES . [ Euc . II . 2 and 3. ] THEOREM 51. [ Euc . II . 4. ] If a straight line is divided in- ternally at any point , the square on the given line is equal to the sum of the squares on the two segments together with twice the ...
... COROLLARIES . [ Euc . II . 2 and 3. ] THEOREM 51. [ Euc . II . 4. ] If a straight line is divided in- ternally at any point , the square on the given line is equal to the sum of the squares on the two segments together with twice the ...
Seite 8
... stated in a theorem is true . 4. The letters Q.E.D. are appended to a theorem , and stand for Quod erat Demonstrandum , which was to be proved . 5. A Corollary is a statement the truth of which 8 GEOMETRY . INTRODUCTORY.
... stated in a theorem is true . 4. The letters Q.E.D. are appended to a theorem , and stand for Quod erat Demonstrandum , which was to be proved . 5. A Corollary is a statement the truth of which 8 GEOMETRY . INTRODUCTORY.
Seite 9
Henry Sinclair Hall. 5. A Corollary is a statement the truth of which follows readily from an established proposition ; it is therefore appended to the proposition as an inference or deduction , which usually requires no further proof ...
Henry Sinclair Hall. 5. A Corollary is a statement the truth of which follows readily from an established proposition ; it is therefore appended to the proposition as an inference or deduction , which usually requires no further proof ...
Seite 10
... OA to its final position OB , the revolving line turns through two right angles , for AOB is a straight line . Hence the L AOC , COB together two right angles . COROLLARY 1. If two straight lines cut one another , 10 GEOMETRY .
... OA to its final position OB , the revolving line turns through two right angles , for AOB is a straight line . Hence the L AOC , COB together two right angles . COROLLARY 1. If two straight lines cut one another , 10 GEOMETRY .
Seite 11
Henry Sinclair Hall. COROLLARY 1. If two straight lines cut one another , the four angles so formed are together equal to four right angles . For example , A B LBOD + 2DOA + LAOC + LCOB = 4 right angles . COROLLARY 2. When any number of ...
Henry Sinclair Hall. COROLLARY 1. If two straight lines cut one another , the four angles so formed are together equal to four right angles . For example , A B LBOD + 2DOA + LAOC + LCOB = 4 right angles . COROLLARY 2. When any number of ...
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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.