Elements of Plane Geometry: For the Use of Schools |
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Page 6
... middle of the three let- ters ; thus the angle ACB , denotes the angle having the vertex C , and contained by the sides AC , BC . The pupil should be careful not to confound an angle with the length of its sides . It is evident , for ...
... middle of the three let- ters ; thus the angle ACB , denotes the angle having the vertex C , and contained by the sides AC , BC . The pupil should be careful not to confound an angle with the length of its sides . It is evident , for ...
Page 35
... middle of the semi - circumfer- ence ADB ; then we have to Fig . 32 . prove that the angle ACD , which is subtended by half the semi - circumference , is a right angle . C A B The arcs AD , DB , are D equal , being each half of a semi ...
... middle of the semi - circumfer- ence ADB ; then we have to Fig . 32 . prove that the angle ACD , which is subtended by half the semi - circumference , is a right angle . C A B The arcs AD , DB , are D equal , being each half of a semi ...
Page 36
... middle of the chord , or the middle of the arc , is perpendicular to the chord . Cor . 2. A perpendicular through the middle of the chord passes through the centre , and through the middle of the arc , and bisects the angle at the ...
... middle of the chord , or the middle of the arc , is perpendicular to the chord . Cor . 2. A perpendicular through the middle of the chord passes through the centre , and through the middle of the arc , and bisects the angle at the ...
Page 40
... middle of the arc AH , and CI to the middle of the arc HE ; then the arc DI will be half of the arc AE ; I E and we have to prove that ABE = DCI . By the preceding case ABH - DCH , and EBH 40 [ BOOK II . INSCRIBED ANGLES .
... middle of the arc AH , and CI to the middle of the arc HE ; then the arc DI will be half of the arc AE ; I E and we have to prove that ABE = DCI . By the preceding case ABH - DCH , and EBH 40 [ BOOK II . INSCRIBED ANGLES .
Page 41
... middle of the arc HE , and CD to the middle of the arc НА . The arc AE is the 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 ...
... middle of the arc HE , and CD to the middle of the arc НА . The arc AE is the 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 ...
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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.