The Elements of GeometryMacmillan, 1886 - 366 sider |
Inni boken
Resultat 1-5 av 46
Side 2
... respectively equal to C and D , is composite , containing the two statements A equals C , and B equals D. 8. Statements that are expressly conditional , such as , if A is B , then C is D , reduce to the typical form as soon as we see ...
... respectively equal to C and D , is composite , containing the two statements A equals C , and B equals D. 8. Statements that are expressly conditional , such as , if A is B , then C is D , reduce to the typical form as soon as we see ...
Side 24
... respectively to the three angles of the other , a pair of equal angles are called Homologous Angles . The pair of sides oppo- site homologous angles are called Homologous Sides . THEOREM VI . 124. Two triangles are congruent if two 24 ...
... respectively to the three angles of the other , a pair of equal angles are called Homologous Angles . The pair of sides oppo- site homologous angles are called Homologous Sides . THEOREM VI . 124. Two triangles are congruent if two 24 ...
Side 25
... respectively to two sides and the included angle in the other . M N I B C A HYPOTHESIS . ABC and LMN two triangles , with AB = LM , BC MN , B = 4 M. CONCLUSION . The two triangles are congruent ; or , using △ for " triangle , " and for ...
... respectively to two sides and the included angle in the other . M N I B C A HYPOTHESIS . ABC and LMN two triangles , with AB = LM , BC MN , B = 4 M. CONCLUSION . The two triangles are congruent ; or , using △ for " triangle , " and for ...
Side 27
... respectively to two angles and the included side in the other . M I А HYPOTHESIS . ABC and LMN two triangles , with A = L , C = N , AC = LN . CONCLUSION . The two triangles are congruent . A ABC & LMN . PROOF . Apply the triangle LMN to ...
... respectively to two angles and the included side in the other . M I А HYPOTHESIS . ABC and LMN two triangles , with A = L , C = N , AC = LN . CONCLUSION . The two triangles are congruent . A ABC & LMN . PROOF . Apply the triangle LMN to ...
Side 28
... respectively to the three sides of the other . N M I C B A HYPOTHESIS . Triangles ABC and LMN , having AB = LM , MN , and CA = NL . BC = CONCLUSION . Δ ΑΒC Ξ Δ ΙΜΝ . PROOF . Imagine △ ABC to be applied to △ LMN in such a way that LN ...
... respectively to the three sides of the other . N M I C B A HYPOTHESIS . Triangles ABC and LMN , having AB = LM , MN , and CA = NL . BC = CONCLUSION . Δ ΑΒC Ξ Δ ΙΜΝ . PROOF . Imagine △ ABC to be applied to △ LMN in such a way that LN ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.