## Elements of Geometry and Trigonometry |

### From inside the book

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Page 11

A The

A The

**rectangle**, which has its angles right angles , without having its sides equal . The parallelogram , or rhomboid , which has its opposite sides parallel . The rhombus , or lozenge , which has its sides equal , without having its ... Page 31

... each of them will be a right angle ; a conclusion which sanctions the seventeenth Definition , where the four angles of a quadrilateral are asserted to be right angles , in the case of the

... each of them will be a right angle ; a conclusion which sanctions the seventeenth Definition , where the four angles of a quadrilateral are asserted to be right angles , in the case of the

**rectangle**and the square . Cor . 2. Page 63

If the given angle is a right angle , the figure will be a

If the given angle is a right angle , the figure will be a

**rectangle**; if , in addition to this , the sides are equal , it will lo be a square . PROBLEM XIII . F To find the centre of a given circle or arc . Page 70

Every parallelogram is equivalent to the

Every parallelogram is equivalent to the

**rectangle**which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the same altitude . a А. Let ABCD be a ... Page 71

The

The

**rectangle**ABCD will contain seven partial**rectangles**, while AEFD will contain four : hence the**rectangle**ABCD is to AEFD as 7 is to 4 , or as AB is to AE . The same reasoning may be applied to any other ratio equally with that of 7 ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude angled triangle base become Book called centre chord circle circumference circumscribed common cone consequently contained corresponding Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar sine solid solid angle sphere spherical triangle square straight line suppose taken tang tangent THEOREM third triangle triangle ABC unit vertex whole

### Popular passages

Page 18 - If two triangles have two sides of the one equal to two sides of the...

Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.

Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...

Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Page 86 - 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 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.

Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.