The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |
From inside the book
Results 1-5 of 13
Page 128
... ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c ...
... ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c ...
Page 261
... ratio of their homologous sides . Let AB , CD be similar parallelopipeds , and the side AE homologous to the side CF : the solid AB shall have to the solid CD , the triplicate ratio of that which AE has to CF. Produce AE , GE , HE ...
... ratio of their homologous sides . Let AB , CD be similar parallelopipeds , and the side AE homologous to the side CF : the solid AB shall have to the solid CD , the triplicate ratio of that which AE has to CF. Produce AE , GE , HE ...
Page 262
... triplicate * ratio of that which it has to the second : therefore the solid AB has to the solid KO , the tripli- cate ratio of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the parallelo- gram GK , and ...
... triplicate * ratio of that which it has to the second : therefore the solid AB has to the solid KO , the tripli- cate ratio of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the parallelo- gram GK , and ...
Page 296
... triplicate ratio of that of their homologous sides . Let the pyramids having the triangles ABC , Def for their bases , and the points G , H for their vertices , be similar , and similarly situated ; the pyramid ABCG shall have to the ...
... triplicate ratio of that of their homologous sides . Let the pyramids having the triangles ABC , Def for their bases , and the points G , H for their vertices , be similar , and similarly situated ; the pyramid ABCG shall have to the ...
Page 297
... triplicate ratio of that which their homologous sides 33. 11 . have : therefore the solid BGML has to the solid EHPO the triplicate ratio of that which the side BC has to the homologous side EF . But as the solid BGML is to the solid ...
... triplicate ratio of that which their homologous sides 33. 11 . have : therefore the solid BGML has to the solid EHPO the triplicate ratio of that which the side BC has to the homologous side EF . But as the solid BGML is to the solid ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
Common terms and phrases
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Popular passages
Page 173 - 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 23 - Any two sides of a triangle are together greater than the third side.
Page 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Page 103 - 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.
Page 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.
Page 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.