Elements of Plane GeometryE.H. Butler & Company, 1882 - 196 σελίδες |
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Σελίδα 19
... ( Ax . 1 ) From each member subtract a . Then △ b = △ ACD , which is impossible . ( Ax . 8 ) .. AC and BC lie in the same straight line . Q. E. D. THEOREM IV . 48. If two straight lines intersect , ELEMENTS OF PLANE GEOMETRY . 19.
... ( Ax . 1 ) From each member subtract a . Then △ b = △ ACD , which is impossible . ( Ax . 8 ) .. AC and BC lie in the same straight line . Q. E. D. THEOREM IV . 48. If two straight lines intersect , ELEMENTS OF PLANE GEOMETRY . 19.
Σελίδα 20
Franklin Ibach. THEOREM IV . 48. If two straight lines intersect , the opposite or vertical angles are equal . Let AB and CD intersect . Ꮯ B To a d A prove that La = Lb. D La + 2c = 2 Ls , ( 44 ) and 2b + 2 c = 2 Ls ; ( 44 ) La + Lc ...
Franklin Ibach. THEOREM IV . 48. If two straight lines intersect , the opposite or vertical angles are equal . Let AB and CD intersect . Ꮯ B To a d A prove that La = Lb. D La + 2c = 2 Ls , ( 44 ) and 2b + 2 c = 2 Ls ; ( 44 ) La + Lc ...
Σελίδα 31
... intersect , as at G. Then and La = Lc , Lb Lc ; - La = Lb . ( 62 ) ( Ax . 1 ) II . Let LM and MN , the sides of d , be respectively || to PQ and OP , the sides of e . To prove that d - = Le . If necessary , produce two sides not I till ...
... intersect , as at G. Then and La = Lc , Lb Lc ; - La = Lb . ( 62 ) ( Ax . 1 ) II . Let LM and MN , the sides of d , be respectively || to PQ and OP , the sides of e . To prove that d - = Le . If necessary , produce two sides not I till ...
Σελίδα 32
... intersect , as at G. Then But La b , and d Le . - Ls b and d are supplements of each other ; Ls a and e are supplements of each other . ( 62 ) Q. E. D. THEOREM XVIII . 70. Two angles having their sides respectively 32 ELEMENTS OF PLANE ...
... intersect , as at G. Then But La b , and d Le . - Ls b and d are supplements of each other ; Ls a and e are supplements of each other . ( 62 ) Q. E. D. THEOREM XVIII . 70. Two angles having their sides respectively 32 ELEMENTS OF PLANE ...
Σελίδα 70
... intersects CF at P , a point whose distance from F equals CF. Likewise we can prove that BE intersects CF at a point whose distance from F equals CF. AD , BE , and CF meet in a common point . Q. E.D. EXERCISES IN INVENTION . THEOREMS ...
... intersects CF at P , a point whose distance from F equals CF. Likewise we can prove that BE intersects CF at a point whose distance from F equals CF. AD , BE , and CF meet in a common point . Q. E.D. EXERCISES IN INVENTION . THEOREMS ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABC and DEF AC and BC acute angle adjacent angles angles are equal angles equals angles formed arc AC BC² bisectors bisects centre CF meet chord common point Concave Polygon construct Convex Polygon COR.-The decagon DEF are similar diagonal BC diameter Draw the diagonal equally distant equals two right equiangular Equilateral Polygon exterior angles given circle given straight line homologous sides hypothenuse included angle intersect La=Lb Let ABCD line joining lines drawn measured by arc medial lines middle point oblique lines parallelogram perimeter PLANE GEOMETRY produced proportion Q. E. D. THEOREM Q. E. F. PROBLEM quadrilateral radii radius rectangle regular inscribed regular polygon respectively equal rhombus right angles right-angled triangle SCHOLIUM secant similar polygons square Subtract tangent third side trapezoid triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 14 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Σελίδα 83 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 85 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 44 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Σελίδα 14 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.
Σελίδα 136 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 55 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.
Σελίδα 137 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 177 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.