## Elements of Geometry and Trigonometry |

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Page 5

41 The Circle and the Measurement of Angles , Problems relating to the First and

41 The Circle and the Measurement of Angles , Problems relating to the First and

**Third**Books , BOOK IV . 57 68 The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth Book , BOOK V. 98 109 Regular ... Page 12

that is to say , when following their perimeters in the same direction , the first side of the one is equal to the first side of the other , the second of the one to the second of the other , the

that is to say , when following their perimeters in the same direction , the first side of the one is equal to the first side of the other , the second of the one to the second of the other , the

**third**to the**third**, and so on . Page 17

DF is equal to AC ; therefore , the point F will fall on C , and the

DF is equal to AC ; therefore , the point F will fall on C , and the

**third**side EF , will coincide with the**third**side BC ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor . Page 18

The sum of any two sides of a triangle , is greater than the

The sum of any two sides of a triangle , is greater than the

**third**side . Let ABC be a triangle : then will the B sum of two of its sides , as AC , CB , be greater than the**third**side AB . For the straight line AB is the shortest ... Page 19

If the point G fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B CE

If the point G fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B CE

**Third**Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem ...### 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.