Elements of Plane Geometry: For the Use of Schools |
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Page 6
... difference of the two angles ABD , CBD . B B 6. When a straight line , as AB , meets another straight line , as CD , so as to make the adjacent angles , CAB , BAD , equal to each other , each of these angles is called a right angle ...
... difference of the two angles ABD , CBD . B B 6. When a straight line , as AB , meets another straight line , as CD , so as to make the adjacent angles , CAB , BAD , equal to each other , each of these angles is called a right angle ...
Page 10
... difference of these quantities , and is read , A minus B. 5. A dot . signifies that the quantities between which it is placed are multiplied together ; thus A.B signifies that A is multiplied by B. 6. The expressions A ( B + C ) , A ( B ...
... difference of these quantities , and is read , A minus B. 5. A dot . signifies that the quantities between which it is placed are multiplied together ; thus A.B signifies that A is multiplied by B. 6. The expressions A ( B + C ) , A ( B ...
Page 39
... difference between OI and NI , is equal to PQ , the difference be- tween IQ and IP ( B. I.Ax. 4 ) . PROP . XI . THEOREM . An inscribed angle is BOOK II . ] ARCS BETWEEN PARALLELS . 39.
... difference between OI and NI , is equal to PQ , the difference be- tween IQ and IP ( B. I.Ax. 4 ) . PROP . XI . THEOREM . An inscribed angle is BOOK II . ] ARCS BETWEEN PARALLELS . 39.
Page 41
... difference of the two arcs H Fig . 40 . B A I E HE , HA ; and the arc DI is the difference of the arcs HI , HD ; but HI is half of HE , and HD is half of HA ; hence DI is half of AE ; and we have to prove that the angles ABE , DCI , are ...
... difference of the two arcs H Fig . 40 . B A I E HE , HA ; and the arc DI is the difference of the arcs HI , HD ; but HI is half of HE , and HD is half of HA ; hence DI is half of AE ; and we have to prove that the angles ABE , DCI , are ...
Page 46
... difference be- H tween two right angles and the sum of A and B ( B. I. Prop . 12 , Cor . 1 ) ; but HIO is the difference be- tween two right angles and the sum of A and B. ( B. I. Prop . 1 , Cor . 1 ) ; hence HIO is the angle required ...
... difference be- H tween two right angles and the sum of A and B ( B. I. Prop . 12 , Cor . 1 ) ; but HIO is the difference be- tween two right angles and the sum of A and B. ( B. I. Prop . 1 , Cor . 1 ) ; hence HIO is the angle required ...
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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.