Elements of Plane Geometry: For the Use of Schools |
From inside the book
Results 1-5 of 21
Page 8
... opposite the right angle is called the hypotenuse . Thus in the triangle ABC , right angled at A , BC is the hypotenuse . 17. The parallelogram is a quadrilateral whose oppo- site sides are parallel . 18. The trapezoid has only two of ...
... opposite the right angle is called the hypotenuse . Thus in the triangle ABC , right angled at A , BC is the hypotenuse . 17. The parallelogram is a quadrilateral whose oppo- site sides are parallel . 18. The trapezoid has only two of ...
Page 13
... opposite angles , formed at their intersection , will be equal . If the lines AB , CD , in- tersect at E , we have to prove that the opposite an- gles CEA , BED , are equal . On account of the straight line CE meeting AB , the angles ...
... opposite angles , formed at their intersection , will be equal . If the lines AB , CD , in- tersect at E , we have to prove that the opposite an- gles CEA , BED , are equal . On account of the straight line CE meeting AB , the angles ...
Page 15
... opposite the equal sides are equal . Let AB , BC , be the equal sides ; then we have to prove that the angle A is equal to C. Fig . 6 . B C D A Draw from B the line BD , so as to divide the angle B into two equal parts ; then in the two ...
... opposite the equal sides are equal . Let AB , BC , be the equal sides ; then we have to prove that the angle A is equal to C. Fig . 6 . B C D A Draw from B the line BD , so as to divide the angle B into two equal parts ; then in the two ...
Page 17
... opposite exterior and interior angles . Cor . 2. A line which is perpendicular to one of two parallels will be perpendicu- lar to the other . Let EF be drawn perpendicular to △ - AB ; now , because it cuts the two parallels , it makes ...
... opposite exterior and interior angles . Cor . 2. A line which is perpendicular to one of two parallels will be perpendicu- lar to the other . Let EF be drawn perpendicular to △ - AB ; now , because it cuts the two parallels , it makes ...
Page 19
... opposite angles . Let the side AB , of the triangle ABC , be produced towards D ; then we have to prove that the exte- rior angle CBD , thus A Fig . 14 . E C B D formed , will be equal to the sum of the interior and oppo- site angles ...
... opposite angles . Let the side AB , of the triangle ABC , be produced towards D ; then we have to prove that the exte- rior angle CBD , thus A Fig . 14 . E C B D formed , will be equal to the sum of the interior and oppo- site angles ...
Other editions - View all
Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast No preview available - 2013 |
Common terms and phrases
ABCD adjacent angles allel alternate angles altitude angle ABC angles ABD angles is equal antecedent and consequent B. I. Ax base centre circle whose radius circumference circumscribed circumscribed circle Converse of Prop describe an arc diagonal diameter divide draw the line equal angles equal B. I. Prop equal chords equal Prop equal respectively equiangular equivalent feet given angle given line given point given side half hence the triangles hypotenuse included angle inscribed angle Let the triangles line drawn linear units longer than AC multiplied number of sides oblique lines parallel to CD parallelogram perimeter perpendicular PROBLEM prove radii rectangle regular polygons respectively equal right angles Prop right-angled triangle Scholium sides AC similar subtended tangent THEOREM three sides triangles ABC triangles are equal vertex
Popular passages
Page 31 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 63 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 70 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 53 - In any proportion, the product of the means is equal to the product of the extremes.
Page 87 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 81 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 61 - 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.
Page 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.