Elements of Plane GeometryE.H. Butler & Company, 1882 - 196 σελίδες |
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Σελίδα 60
... A diagonal of a parallelogram divides it into two equal triangles . 130. COR . 2. - Parallels intercepted between parallels are equal . THEOREM XLI . 131. Two parallelograms are equal if two 60 ELEMENTS OF PLANE GEOMETRY . PARALLELOGRAMS.
... A diagonal of a parallelogram divides it into two equal triangles . 130. COR . 2. - Parallels intercepted between parallels are equal . THEOREM XLI . 131. Two parallelograms are equal if two 60 ELEMENTS OF PLANE GEOMETRY . PARALLELOGRAMS.
Σελίδα 66
... intercepted between the sides equals half the base . In the ABC , let DE be II to the base AB and bisect AC at D. C D / c Ε b A a F I. To prove that DE bisects BC . Let DF bell to BC . B La = Lc , Lb - Ld , ( 62 ) ( 62 ) and AD DC ...
... intercepted between the sides equals half the base . In the ABC , let DE be II to the base AB and bisect AC at D. C D / c Ε b A a F I. To prove that DE bisects BC . Let DF bell to BC . B La = Lc , Lb - Ld , ( 62 ) ( 62 ) and AD DC ...
Σελίδα 100
... intercepted by angles at the centre are to each other as the angles . 205. SCHOLIUM . - The truth of this proposition gave rise to the method of measuring angles by arcs . It will be observed , that if arcs are struck with the same ...
... intercepted by angles at the centre are to each other as the angles . 205. SCHOLIUM . - The truth of this proposition gave rise to the method of measuring angles by arcs . It will be observed , that if arcs are struck with the same ...
Σελίδα 101
... intercepted arc . In the O ABC , let AB and CB be the sides of the in- scribed a . CASE I. - Let the centre O be in one of the sides . α B To prove that a is measured by arc AC . Draw the radius OA . OA = ов ; ( 182 ) AABO is isosceles ...
... intercepted arc . In the O ABC , let AB and CB be the sides of the in- scribed a . CASE I. - Let the centre O be in one of the sides . α B To prove that a is measured by arc AC . Draw the radius OA . OA = ов ; ( 182 ) AABO is isosceles ...
Σελίδα 104
... intercepted arc . Let the ABD be formed by the tangent CD and the chord AB . C A a B D To prove that ABD is measured by arc AEB . Draw the diameter BE . ba L , ( 195 ) and is measured by arc EB , ( 208 ) anda is measured by arc AE ...
... intercepted arc . Let the ABD be formed by the tangent CD and the chord AB . C A a B D To prove that ABD is measured by arc AEB . Draw the diameter BE . ba L , ( 195 ) and is measured by arc EB , ( 208 ) anda is measured by arc AE ...
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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.