Elementary Geometry: Practical and TheoreticalUniversity Press, 1903 - 355 Seiten |
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Ergebnisse 1-5 von 73
Seite x
... data 113 Miscellaneous Exercises 115 Inequalities 119 Parallelograms 132 Subdivision of a straight line 140 Loci 143 Intersection of loci 148 Coordinates 152 Miscellaneous Exercises 154 Book II . AREA . Area by counting squares ...
... data 113 Miscellaneous Exercises 115 Inequalities 119 Parallelograms 132 Subdivision of a straight line 140 Loci 143 Intersection of loci 148 Coordinates 152 Miscellaneous Exercises 154 Book II . AREA . Area by counting squares ...
Seite 65
... Data To prove that △ BOA + LAOC = 2 rt . 4 S. Construction Draw OD to represent the line through O per- pendicular to BC . Proof L BOA = 4 BOD + LAOC = 4 DOC - DOA , △ DOA , .. 4 BOA + AOC = 4 BOD + DOC = 2 rt . 2 s . Constr ...
... Data To prove that △ BOA + LAOC = 2 rt . 4 S. Construction Draw OD to represent the line through O per- pendicular to BC . Proof L BOA = 4 BOD + LAOC = 4 DOC - DOA , △ DOA , .. 4 BOA + AOC = 4 BOD + DOC = 2 rt . 2 s . Constr ...
Seite 67
... Data The sum of the adjacent s BOA , AOC = 2 rt . ≤ s . Το prove that Construction Proof BOC is a straight line . Produce BO to D. Since AO meets the st . line BD at O , ..L BOA + L AOD = 2 rt . 4 s . But BOA + 4 AOC = 2 rt . Ls , ..L ...
... Data The sum of the adjacent s BOA , AOC = 2 rt . ≤ s . Το prove that Construction Proof BOC is a straight line . Produce BO to D. Since AO meets the st . line BD at O , ..L BOA + L AOD = 2 rt . 4 s . But BOA + 4 AOC = 2 rt . Ls , ..L ...
Seite 69
... Data Two st . lines intersect forming the angles x , y , z , w . To prove that Proof Revise Ex . 67 , 68 . Lx vert . opp . 4 % , Ly = vert . opp . △ w . 4x + 2y = 2rt . 4s , ( Why ? ) Ly + Lz = 2rt . 4s , ( Why ? ) .. Lx + LY = Ly + LZ ...
... Data Two st . lines intersect forming the angles x , y , z , w . To prove that Proof Revise Ex . 67 , 68 . Lx vert . opp . 4 % , Ly = vert . opp . △ w . 4x + 2y = 2rt . 4s , ( Why ? ) Ly + Lz = 2rt . 4s , ( Why ? ) .. Lx + LY = Ly + LZ ...
Seite 71
... Data The st . line EF cuts the two st . lines AB , CD at E , F , forming the 4s a , b , c , d ; and a = alternate △ d . Το prove that Proof AB , CD are parallel . La + b = 2 rt . s , I. 1 . Lc + Ld = 2 rt . s , I. 1 . :: La + 2b = Lc + ...
... Data The st . line EF cuts the two st . lines AB , CD at E , F , forming the 4s a , b , c , d ; and a = alternate △ d . Το prove that Proof AB , CD are parallel . La + b = 2 rt . s , I. 1 . Lc + Ld = 2 rt . s , I. 1 . :: La + 2b = Lc + ...
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Elementary Geometry: Practical and Theoretical Charles Godfrey,Arthur Warry Siddons Keine Leseprobe verfügbar - 2015 |
Elementary Geometry: Practical and Theoretical C. Godfrey,A. W. Siddons Keine Leseprobe verfügbar - 2020 |
Häufige Begriffe und Wortgruppen
AABC altitude base BC bisects Calculate centimetres centre chord circle of radius circumcentre circumcircle circumference circumscribed common tangent concyclic Constr Construct a triangle Construction Proof cyclic quadrilateral diagonal diameter distance divided Draw a circle Draw a straight equal circles equiangular equidistant equilateral triangle equivalent find a point Find the area fixed point Give a proof given circle given line given point given straight line hypotenuse inch paper inscribed intersect isosceles trapezium isosceles triangle LAOB LAPB locus of points Measure meet miles opposite sides parallelogram Plot the locus polygon produced protractor Q. E. D. Ex quadrilateral ABCD radii rect rectangle contained reflex angle Repeat Ex rhombus right angles right-angled triangle segment set square similar triangles subtends tangent THEOREM trapezium triangle ABC units of length vertex vertical angle
Beliebte Passagen
Seite 88 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Seite 269 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Seite 206 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 342 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Seite 270 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Seite 186 - This sub-division shows that the square on the hypotenuse of the above right-angled triangle is equal to the sum of the squares on the sides containing the right angle.
Seite 206 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Seite 136 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Seite 214 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Seite 123 - The difference between any two sides of a triangle is less than the third side.