The Elements of GeometryMacmillan, 1886 - 366 Seiten |
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Seite 5
... corollary to a theorem is a statement whose truth follows at once from that of the theorem , or from what has been given in the demonstration of the theorem . - 27. A theorem consists of two parts , the hypothesis , or that which is ...
... corollary to a theorem is a statement whose truth follows at once from that of the theorem , or from what has been given in the demonstration of the theorem . - 27. A theorem consists of two parts , the hypothesis , or that which is ...
Seite 19
... COROLLARY . ( 93. Halves of equals are equal . ) From a point on a line , there cannot be more than one perpendicular to that line . THEOREM II . 106. All perigons are equal . C 0 丸 HYPOTHESIS . CONCLUSION . G H ↑ D AOA is a perigon ...
... COROLLARY . ( 93. Halves of equals are equal . ) From a point on a line , there cannot be more than one perpendicular to that line . THEOREM II . 106. All perigons are equal . C 0 丸 HYPOTHESIS . CONCLUSION . G H ↑ D AOA is a perigon ...
Seite 21
... COROLLARY . The four bisectors of the four angles . formed by two lines intersecting , form a pair of lines perpen- dicular to each other . II . Angles about Two Points . III . A RELATIONS of lines , angles , AND TRIANGLES . 21.
... COROLLARY . The four bisectors of the four angles . formed by two lines intersecting , form a pair of lines perpen- dicular to each other . II . Angles about Two Points . III . A RELATIONS of lines , angles , AND TRIANGLES . 21.
Seite 26
... COROLLARY . Every equilateral triangle is also equi- angular . EXERCISES . 2. The bisectors of vertical angles are in the same line . THEOREM VIII . 128. Two triangles are congruent if two 26 THE ELEMENTS OF GEOMETRY .
... COROLLARY . Every equilateral triangle is also equi- angular . EXERCISES . 2. The bisectors of vertical angles are in the same line . THEOREM VIII . 128. Two triangles are congruent if two 26 THE ELEMENTS OF GEOMETRY .
Seite 34
... COROLLARY I. The line drawn to bisect the angle at the vertex of an isosceles triangle , also bisects the base , and is perpendicular to it . 138. COROLLARY II . The line drawn from the vertex of an isosceles triangle to bisect the base ...
... COROLLARY I. The line drawn to bisect the angle at the vertex of an isosceles triangle , also bisects the base , and is perpendicular to it . 138. COROLLARY II . The line drawn from the vertex of an isosceles triangle to bisect the base ...
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Häufige Begriffe und Wortgruppen
ABCD alternate angles altitude angles are equal angles equal angles opposite base bisect called chord circumcenter coincide common commutative law CONCLUSION construction COROLLARY cross-ratio describe diagonals diameter divided draw equal are congruent equal sects equiangular equivalent exterior angle figure given line given point given sect greater greatest common divisor hypothenuse HYPOTHESIS included angle inscribed inscribed angle intercepted interior intersecting lines isosceles triangle less locus magnitudes meet mid-point multiples number of sides pair parallelogram pass perigon perimeter perpendicular bisector plane MN prismatoid PROOF proportional quadrilateral radii radius ratio rectangle rectangle contained regular polygon respectively equal rhombus right angle Rule of Inversion sect joining segment sides equal sphere spherical polygon square straight angle subtended supplemental surface symmetrical tangent THEOREM THEOREM VIII three sides transversal triangles are congruent vertex
Beliebte Passagen
Seite 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Seite 112 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Seite 190 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Seite 13 - An Acute Angle is one which is less than a right angle.
Seite 104 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Seite 107 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Seite 103 - 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.