## Elements of Geometry and Trigonometry |

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Page 19

triangle GAC is equal to DEF , since , by construction , they have an equa angle in each ,

triangle GAC is equal to DEF , since , by construction , they have an equa angle in each ,

**contained**by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the ... Page 34

If the other magnitude

If the other magnitude

**contain**a certain number of those units , it also may be expressed by the number of its units ... there may perhaps be a smaller unit which will be**contained**an exact number of times in each of the magnitudes . Page 51

In the same circle , or in equal circles , equal angles having their vertices at the centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles

In the same circle , or in equal circles , equal angles having their vertices at the centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles

**contained**by the radii will also ... Page 52

Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is

Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is

**contained**7 times in the angle ACB , and 4 times in ... Page 60

...

...

**contain**, being given , to describe the triangle . Let the lines B and C be equal to TB TC TE the given sides , and A the given angle . Having drawn the indefinite line DE , at the point D , make the angle EDF equal to the given ...### 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.