The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as], Part 3

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Page 132 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Page 28 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Page 115 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...
Page 6 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Page 100 - 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 4 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Page 22 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 120 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 160 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 30 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

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