The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : 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 : to this Edition are Also Annexed, Elements of Plane and Spherical Trigonometry

Robert Desilver, 1821 - 516 من الصفحات

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المحتويات

 القسم 1 i القسم 2 iii القسم 3 7 القسم 4 9 القسم 5 49 القسم 6 88 القسم 7 100 القسم 8 117
 القسم 16 250 القسم 17 261 القسم 18 271 القسم 19 272 القسم 20 274 القسم 21 276 القسم 22 283 القسم 23 285

 القسم 9 153 القسم 10 190 القسم 11 191 القسم 12 194 القسم 13 224 القسم 14 230 القسم 15 240
 القسم 24 286 القسم 25 290 القسم 26 293 القسم 27 295 القسم 28 365 القسم 29 461 القسم 30 491

مقاطع مشهورة

الصفحة 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
الصفحة 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
الصفحة 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
الصفحة 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
الصفحة 9 - 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.
الصفحة 55 - If 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.
الصفحة 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 of the line between the points of section, is equal to the square of half the line.
الصفحة 318 - 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.
الصفحة 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
الصفحة 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.