# The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's Data

Bell & Bradfute, 1835 - 513 من الصفحات

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### المحتويات

 The ELEMENTs of EUCLID 11 Notes on the Elements 283 Euclids DATA 349 º Notes on the Data 445
 PLANE TRIGonoMETRY 461 w Rules for Plane Triangles 473 SPHERICAL TRIGoNoMETRY 483

### مقاطع مشهورة

الصفحة 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
الصفحة 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.
الصفحة 306 - 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 11 - 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 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
الصفحة 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
الصفحة 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
الصفحة 26 - IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite, upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
الصفحة 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
الصفحة 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.