## A System of Popular Geometry: Containing in a Few Lessons So Much of the Elements of Euclid as is Necessary and Sufficient for a Right Understanding of Every Art and Science in Its Leading Truths and General PrinciplesTaylor and Walton, Booksellers to the University of London, 30 Upper Gower Street, 1836 - Euclid's Elements - 128 pages |

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ABCD acute altitudes angle ABC angles BAC angles equal arch base Book called centre chord circle circumference common Consequently contained corresponding definition demonstration described difference distant divided double draw drawn Elements equal angles Euclid evident exactly extremities fall false figure fourth Geometry given given point greater half Hence ibid internal angles Join latter less Let ABC lines be drawn magnitude manner mean meet Note opposite parallel parallelogram pass perpendicular plane preceding present PROB problem produced proof propositions proved quantities ratio reader rectangle rectilineal remaining respectively equal right angles right line Science segments side ac square stand submultiple suppose supposition surface taken tangent theorem things triangles ABC unequal vertex whole wholly

### Popular passages

Page 31 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.

Page xxxi - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Page 3 - If two triangles have two sides of the 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 xxx - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 30 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.

Page 25 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.

Page 99 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.

Page 51 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...

Page 11 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page 11 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.