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abcd added alternate altitude angle abc angle acb base bisect Book centre chord circle circle abc circumference common consequently Const contained demonstration describe desinition diagonal diameter difference distance divided double draw drawn Elements equal equiangular equimultiples Euclid fall fame manner fame multiple fame ratio former four given given right line greater half inscribed intersect join the points less Let abc magnitudes mean meet parallel parallelogram pass perpendicular plane polygon prism Problem produced PROP proportional proposition proved Q.E.D. PROP reason rectangle rectangle of ac remaining angle right angles right line segment shewn side side ac sigure similar sirst solid squares of ac stand taken tangent Theorem thing third triangle triangle abc VIII whence whole
Strona 166 - 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.
Strona 71 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Strona 207 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Strona 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Strona 241 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Strona 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.
Strona 135 - If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest.
Strona 145 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.