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

Conrad and Company, 1892 - 518 من الصفحات

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المحتويات

 BOOK 1 DEFINITIONs Postulates AXIOMs 10 PARALLELS AND PARALLELoGIRAMs 27 THE AREAs of PARALLELoG1 AMS AND TRIANGLEs 35 ANALYSIs SYNTHESIS 87 ON PARALLELs 95 WII ON THE CONSTRUCTION or TRIANGLEs witH GIVEN 107 BOOK III 149
 Theorems and E camples on Book IV 277 PR00Fs of THE PROPOSITIONS DERIVED FROM THE GEOMETRicAL 297 BOOK 307 ON HARMONIC SECTION 359 ON Polk AND Polar 365 371 371 WI MISCELLANEous ExAMPLEs on Book VI 377 BOOK XI 383

 amples on Book III 215 BOOK IV 250
 ExERCISEs on Book XI 418

مقاطع مشهورة

الصفحة 333 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
الصفحة 1 - 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.
الصفحة 45 - 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 142 - In every triangle, the square on the side subtending an acute angle, 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 perpendicular let fall on it from the opposite angle, and the acute angle.
الصفحة 148 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
الصفحة 377 - 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 308 - From this it is manifest, that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
الصفحة 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.
الصفحة 73 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
الصفحة 7 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.