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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...
Visualització completa - 1838
AC is equal altitude angle ABC angle BAC base base BC bisect Book centre circle ABCD circumference common cone contained cylinder demonstrated described diameter divided double draw EFGH equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prisms PROB produced proportionals proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure remaining angle right angles segment sides similar solid solid angle sphere square taken THEOR third touch triangle ABC vertex wherefore whole
Pàgina 171 - 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.
Pàgina 56 - 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.
Pàgina 53 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Pàgina 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Pàgina 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Pàgina 23 - Any two sides of a triangle are together greater than the third side.
Pàgina 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Pàgina 101 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.
Pàgina 50 - PROP. I. THEOR. If there oe 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.