The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson].
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Σελίδα 43 - 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.
Σελίδα 20 - Any two sides of a triangle are together greater than the third side.
Σελίδα 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 310 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.
Σελίδα 153 - 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.
Σελίδα 52 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 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.
Σελίδα 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.