Elements of Plane Geometry |
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Page 31
Franklin Ibach. EQUALITY OF ANGLES . THEOREM XVI . 68. Two angles are equal if their sides are respectively parallel and lying in the same or in opposite directions from their vertices . I. Let AB and BC , the sides of a , be respectively ...
Franklin Ibach. EQUALITY OF ANGLES . THEOREM XVI . 68. Two angles are equal if their sides are respectively parallel and lying in the same or in opposite directions from their vertices . I. Let AB and BC , the sides of a , be respectively ...
Page 33
Franklin Ibach. THEOREM XVIII . 70. Two angles having their sides respectively perpendicular to each other are either equal ... respectively to ED and EF , and let GN be drawn || to EF or BM . Then and Le = Lb , Ze is the supplement of ...
Franklin Ibach. THEOREM XVIII . 70. Two angles having their sides respectively perpendicular to each other are either equal ... respectively to ED and EF , and let GN be drawn || to EF or BM . Then and Le = Lb , Ze is the supplement of ...
Page 39
... respectively equal to two angles of another , the third angles are also equal . 79. COR . 3. — In any triangle , there can be but one right angle , or but one obtuse angle . 80. COR . 4. - In any right - angled triangle , the sum of the ...
... respectively equal to two angles of another , the third angles are also equal . 79. COR . 3. — In any triangle , there can be but one right angle , or but one obtuse angle . 80. COR . 4. - In any right - angled triangle , the sum of the ...
Page 41
Franklin Ibach. EQUALITY OF TRIANGLES . THEOREM XXIV . 83. Two triangles are equal in all their parts if two sides and the included angle of the one are respectively equal to two sides and the included angle of the other . 1 = In the As ...
Franklin Ibach. EQUALITY OF TRIANGLES . THEOREM XXIV . 83. Two triangles are equal in all their parts if two sides and the included angle of the one are respectively equal to two sides and the included angle of the other . 1 = In the As ...
Page 42
... equal to two angles and the included side of the other . In the As ABC and DEF , let a = d , Lb Le , and AB = DE ... respectively equal to the corresponding parts of another triangle , the triangles are equal . THEOREM XXVI . 86 ...
... equal to two angles and the included side of the other . In the As ABC and DEF , let a = d , Lb Le , and AB = DE ... respectively equal to the corresponding parts of another triangle , the triangles are equal . THEOREM XXVI . 86 ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 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.
Page 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.
Page 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.