Elements of Plane Geometry: For the Use of Schools |
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Page 8
... all equal . 20. A rectangle is a par- allelogram having all its an- gles right angles . 21. A square is a rectan- gle having all its sides equal . 22. A diagonal is a line which joins the vertices 8 [ BOOK I. DEFINITIONS .
... all equal . 20. A rectangle is a par- allelogram having all its an- gles right angles . 21. A square is a rectan- gle having all its sides equal . 22. A diagonal is a line which joins the vertices 8 [ BOOK I. DEFINITIONS .
Page 9
For the Use of Schools Nicholas Tillinghast. 22. A diagonal is a line which joins the vertices of two angles which are not ad- jacent to each other . Thus AC , AD , AE , AF , are diagonals . E D B C 23. Plane figures are equal , when ...
For the Use of Schools Nicholas Tillinghast. 22. A diagonal is a line which joins the vertices of two angles which are not ad- jacent to each other . Thus AC , AD , AE , AF , are diagonals . E D B C 23. Plane figures are equal , when ...
Page 28
... diagonal DB . Now because A Fig . 26 . B AB , DC , are parallel , the angles ABD , BDC , are equal , and because D C AD , BC , are parallel , the angles ADB , DBC , are equal ( Prop . 9 ) ; then the triangles ABD , CDB , having the two ...
... diagonal DB . Now because A Fig . 26 . B AB , DC , are parallel , the angles ABD , BDC , are equal , and because D C AD , BC , are parallel , the angles ADB , DBC , are equal ( Prop . 9 ) ; then the triangles ABD , CDB , having the two ...
Page 29
For the Use of Schools Nicholas Tillinghast. Draw the diagonal DB ; then in the triangles ABD , BCD , we have AB = DC , AD = BC , and BD com- mon ; hence these triangles are equal ( Prop . 22 ) ... diagonal DB; then in the triangles ABD...
For the Use of Schools Nicholas Tillinghast. Draw the diagonal DB ; then in the triangles ABD , BCD , we have AB = DC , AD = BC , and BD com- mon ; hence these triangles are equal ( Prop . 22 ) ... diagonal DB; then in the triangles ABD...
Page 62
... diagonal DB . EF is the altitude of the tri- angle ABD with AB taken as the base ; and is also the A Fig . 63 . D E C altitude of DBC with DC taken as a base . B Now the area of the trapezoid is equal to the sum of the areas of the two ...
... diagonal DB . EF is the altitude of the tri- angle ABD with AB taken as the base ; and is also the A Fig . 63 . D E C altitude of DBC with DC taken as a base . B Now the area of the trapezoid is equal to the sum of the areas of the two ...
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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.