The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |
From inside the book
Results 1-5 of 38
Page i
... Fourth Edition . 18mo . cloth . 48. 6d . Key to the Mechanics for Beginners . Crown 8vo . cloth . 6s . 6d . Algebra for the use of Colleges and Schools . With numerous Examples . New Edition . Crown 8vo . cloth . 73. 6d . Key to the ...
... Fourth Edition . 18mo . cloth . 48. 6d . Key to the Mechanics for Beginners . Crown 8vo . cloth . 6s . 6d . Algebra for the use of Colleges and Schools . With numerous Examples . New Edition . Crown 8vo . cloth . 73. 6d . Key to the ...
Page 134
... fourth , when any equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is ...
... fourth , when any equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is ...
Page 135
... fourth ; and the third is said to have to the fourth a less ratio than the first has to the second . 8. Analogy , or proportion , is the similitude of ratios . 9. Proportion consists in three terms at least . 10. When three magnitudes ...
... fourth ; and the third is said to have to the fourth a less ratio than the first has to the second . 8. Analogy , or proportion , is the similitude of ratios . 9. Proportion consists in three terms at least . 10. When three magnitudes ...
Page 136
... fourth . V. 16 . 14. Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is to the first as the fourth is to the third . V. B. 15. Componendo , by composition ; when there are four ...
... fourth . V. 16 . 14. Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is to the first as the fourth is to the third . V. B. 15. Componendo , by composition ; when there are four ...
Page 137
... fourth of the first rank , as the last but three is to the last but two of the second rank ; and so on in a cross order ; and the inference is that mentioned in the eighteenth definition . V. 23 . AXIOMS . 1. Equimultiples of the same ...
... fourth of the first rank , as the last but three is to the last but two of the second rank ; and so on in a cross order ; and the inference is that mentioned in the eighteenth definition . V. 23 . AXIOMS . 1. Equimultiples of the same ...
Other editions - View all
Common terms and phrases
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Popular passages
Page 262 - 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.
Page 71 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Page 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Page 182 - 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 8 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Page 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Page 58 - 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.
Page 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Page 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Page 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.