Elements of Plane GeometryE.H. Butler & Company, 1882 - 196 σελίδες |
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Σελίδα 3
... BETWEEN THE PARTS OF A TRIANGLE 48 BISECTORS OF ANGLES 51 POLYGONS 54 • ANGLES OF A POLYGON QUADRILATERALS . PARALLELOGRAMS 56 58 60 EXERCISES IN INVENTION 71 DEFINITIONS THEOREMS DEFINITIONS BOOK II . RATIO AND PROPORTION . 3.
... BETWEEN THE PARTS OF A TRIANGLE 48 BISECTORS OF ANGLES 51 POLYGONS 54 • ANGLES OF A POLYGON QUADRILATERALS . PARALLELOGRAMS 56 58 60 EXERCISES IN INVENTION 71 DEFINITIONS THEOREMS DEFINITIONS BOOK II . RATIO AND PROPORTION . 3.
Σελίδα 50
... so as to make a = L c . Then AD = CD . ( 98 ) Now AD + BD > AB . ( Ax . 11 ) Substitute CD for its equal AD . Then or CD + BD > AB , BC > AB . Q. E. D. BISECTORS OF ANGLES . THEOREM XXXV . 101. Any point 50 ELEMENTS OF PLANE GEOMETRY .
... so as to make a = L c . Then AD = CD . ( 98 ) Now AD + BD > AB . ( Ax . 11 ) Substitute CD for its equal AD . Then or CD + BD > AB , BC > AB . Q. E. D. BISECTORS OF ANGLES . THEOREM XXXV . 101. Any point 50 ELEMENTS OF PLANE GEOMETRY .
Σελίδα 51
Franklin Ibach. BISECTORS OF ANGLES . THEOREM XXXV . 101. Any point in the bisector of an angle is equally distant from the sides of the angle . Let BF be the bisector of the ABC , Pany point in it , and PD and PE Ls to AB and BC . D 10 ...
Franklin Ibach. BISECTORS OF ANGLES . THEOREM XXXV . 101. Any point in the bisector of an angle is equally distant from the sides of the angle . Let BF be the bisector of the ABC , Pany point in it , and PD and PE Ls to AB and BC . D 10 ...
Σελίδα 52
... bisectors AE , BF , and CD meet in a common point . Q. E. D. 104. COR . - The point in which the bisectors of the angles of a triangle meet is equally distant from the three sides of the triangle . THEOREM XXXVII . 105. The ...
... bisectors AE , BF , and CD meet in a common point . Q. E. D. 104. COR . - The point in which the bisectors of the angles of a triangle meet is equally distant from the three sides of the triangle . THEOREM XXXVII . 105. The ...
Σελίδα 71
... bisected , the triangle formed by the bisectors and the base is an isos- celes triangle . 5. The three straight lines joining the middle points of the sides of a triangle divide the triangle into four equal tri- angles . 6. If one of ...
... bisected , the triangle formed by the bisectors and the base is an isos- celes triangle . 5. The three straight lines joining the middle points of the sides of a triangle divide the triangle into four equal tri- angles . 6. If one of ...
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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.