## A Text-book of Geometry |

### From inside the book

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Page 98

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**arcs**. B በዚ CASE I. When the**arcs**are commensurable . In the**circles**whose centres are C and D , let ACB and EDF be the angles , AB and EF the intercepted**arcs**. To prove ZACB**arc**AB LEDF**arc**EF Proof . Let m be a common**measure**of AB ... Page 99

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**arc**AB**arc**A'B ' Proof . Divide AB into any number of equal parts , and apply one of these parts as a unit of**measure**...**measure**is indefinitely diminished , these ratios continue equal , and approach indefinitely the limiting ratios ... Page 100

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**measured**by its intercepted**arc**; meaning , An angle at the centre is such a part of the whole angular magnitude about the centre as its intercepted**arc**is of the whole**circumference**. PROPOSITION XVII . THEOREM . 263. An inscribed ... Page 101

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**measured by arc**EA . Draw the diameter BCP . PBA is**measured by arc**PA , Case I. ZPBE is**measured by arc**PE , Case I. ( arc PA + arc PE ) , arc EA . :: ZPBA + Z PBE is measured by or ZEBA is measured by CASE III . When the centre is ... Page 102

... measured by one - half the sum of the intercepted arcs . Ө Let the angle AOC be formed by the chords AB and CD . To ... arc AC , $ 263 and A is

... measured by one - half the sum of the intercepted arcs . Ө Let the angle AOC be formed by the chords AB and CD . To ... arc AC , $ 263 and A is

**measured by arc**BD , ( an inscribed is measured by the intercepted arc ) . ..Z COA is ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē acute angle altitude angles are equal apothem base bisector bisects called centre chord circumference circumscribed circumscribed circle coincide decagon diagonal diameter divide Draw equal angles equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angles feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersect isosceles trapezoid isosceles triangle legs length line joining measured by arc middle points number of sides parallel parallelogram perimeter perpendicular prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments shortest side similar polygons straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices

### Popular passages

Page 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 144 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 130 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.

Page 128 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 211 - 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 157 - 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 152 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 187 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.

Page 136 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.