The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 páginas |
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Página 7
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are ...
Página 126
... magnitudes of the same kind to one another , in respect of quantity . " 66 IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to ...
... magnitudes of the same kind to one another , in respect of quantity . " 66 IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to ...
Página 127
... Magnitudes which have the same ratio are called pro- portionals . N. B. When four magnitudes are pro- • portionals , it is usually expressed by saying , the ' first is to the second , as the third to the fourth . ' VII . When of the ...
... Magnitudes which have the same ratio are called pro- portionals . N. B. When four magnitudes are pro- • portionals , it is usually expressed by saying , the ' first is to the second , as the third to the fourth . ' VII . When of the ...
Página 128
Euclides William Rutherford. X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first ...
Euclides William Rutherford. X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first ...
Página 129
... magnitude of proportionals , so that they continue ' still to be proportionals . ' XIII . Permutando , or alternando , by permutation , or alter- nately . This word is used when there are four proportionals , and it is inferred , that ...
... magnitude of proportionals , so that they continue ' still to be proportionals . ' XIII . Permutando , or alternando , by permutation , or alter- nately . This word is used when there are four proportionals , and it is inferred , that ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Sin vista previa disponible - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid Sin vista previa disponible - 2023 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 23 - Any two sides of a triangle are together greater than the third side.
Página 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Página 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.
Página 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.
Página 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.