The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
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Seite 161
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less , that is , " when the greater contains the less a certain number of times exactly . " 3 . " Ratio is a mutual relation of two magnitudes ...
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less , that is , " when the greater contains the less a certain number of times exactly . " 3 . " Ratio is a mutual relation of two magnitudes ...
Seite 166
Because AB is the same multiple of C that DE is of F ; с A B 1 In like manner , therefore с F G F D D 1. There are as many magnitudes in AB equal to C , as there are in DE equal to F. E I 2. There are as many magnitudes in BG equal to C ...
Because AB is the same multiple of C that DE is of F ; с A B 1 In like manner , therefore с F G F D D 1. There are as many magnitudes in AB equal to C , as there are in DE equal to F. E I 2. There are as many magnitudes in BG equal to C ...
Seite 170
Because AG is the same multiple of E , that CH is of F ( hyp . ) , and that GB is equal to E , and CK to F ; therefore 1. AB is the same multiple of E , that KH is of F ; 2. KH is equal to CD ( V. Ax . 1 ) ; take away the common ...
Because AG is the same multiple of E , that CH is of F ( hyp . ) , and that GB is equal to E , and CK to F ; therefore 1. AB is the same multiple of E , that KH is of F ; 2. KH is equal to CD ( V. Ax . 1 ) ; take away the common ...
Seite 172
If the first be the same multiple of the second , or the same part of it , that the third is of the fourth ; the first is to the second , as the third is to the fourth . First . Let the first A be the same multiple of the second B ...
If the first be the same multiple of the second , or the same part of it , that the third is of the fourth ; the first is to the second , as the third is to the fourth . First . Let the first A be the same multiple of the second B ...
Seite 174
B is to A , as D to C ( V. B ) ; but A is a part of B , therefore B is a multiple of A ( hyp . ) ; therefore , by the preceding case , D is the same multiple of C ; that is , 2. C is the same part of D , that A is of B. Therefore ...
B is to A , as D to C ( V. B ) ; but A is a part of B , therefore B is a multiple of A ( hyp . ) ; therefore , by the preceding case , D is the same multiple of C ; that is , 2. C is the same part of D , that A is of B. Therefore ...
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD AC is equal alternate angle ABC angle ACB angle BAC base base BC bisected centre circle ABC circumference common compounded constr Construction Demonstration describe diameter divided double draw equal angles equiangular equimultiples exterior angle extremities fall fore four fourth given point given straight line greater half inscribed interior join less Let ABC likewise magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular plane polygon produced Proof proportionals proved Q.E.D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square on AC straight line BC taken third touches the circle triangle ABC unequal wherefore whole
Beliebte Passagen
Seite 1 - 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.
Seite 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Seite 112 - 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.
Seite 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 269 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 199 - 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.
Seite 23 - 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.
Seite 63 - 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...
Seite 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Bibliografische Informationen
| Titel | The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
| Autor/in | Euclides |
| Herausgeber | James Martin (of the Wedgwood inst, Burslem) |
| Veröffentlicht | 1874 |
| Original von | Oxford University |
| Digitalisiert | 8. Sept. 2006 |
| Zitat exportieren | BiBTeX EndNote RefMan |