## Elements of geometry, with ... trigonometry |

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### Common terms and phrases

base base and altitude bisect called centre chord circle circumference circumscribed coincide common cone consequently constructed contained cylinder described diagonals diameter dicular difference distance divided draw drawn edges equal equal angles equidistant equilateral equivalent expressed extremities fall feet figure four given circle given line given point greater Hence homologous hypothenuse indefinite inscribed intersection joining lateral less locus mean measured meet oblique opposite sides parallel planes parallelogram pass perimeter perpen perpendicular plane MN polygon prism proportional pyramid quadrilateral radii radius rectangle regular polygon remainder represented respectively right angle right-angled triangle sector segment sides similar solid sphere square straight line surface Take tangent THEOREM third triangle triangular vertex vertices volume

### Popular passages

Page 62 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or...

Page 12 - Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Page 62 - ... and any equimultiples whatsoever of the second and fourth, if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...

Page 106 - The area of a triangle is equal to half the product of its base by its altitude.

Page 90 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

Page 71 - 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, minus twice the product of one of these sides and the projection of the other side upon it.

Page 103 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 70 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 58 - The square described on a straight line drawn from one of the angles at the base of a triangle to the middle point of the opposite side, is equal to the sum or difference of the square...

Page 106 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.