## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |

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AC is equal alfo angle ABC angle BAC bafe BC is given becaufe bisected circle ABCD circumference cone cylinder demonstrated Desinition diameter draw drawn E. D. PROP equal angles equiangular equimultiples Euclid faid fame altitude fame manner fame multiple fame ratio fame reason fecond fhall fhewn fides firft fore fquare ftraight given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join lefs less Let ABC P R O parallel parallelepipeds parallelogram perpendicular polygon prism proportionals Proposition pyramid rectangle contained rectilineal sigure right angles segment sides similar sine sirst solid angle square of AC straight line BC T H E O tiple triangle ABC vertex wherefore

### Popular passages

Page 156 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.

Page 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Page 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Page 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Page 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Page 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...