Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Seite 115
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first is greater than the multiple of the second , equal to it , or less , so is the multiple of the third ...
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first is greater than the multiple of the second , equal to it , or less , so is the multiple of the third ...
Seite 116
... multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ...
... multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ...
Seite 118
... multiple of A by m . So m ( A + B ) is a multiple of A + B by m ; m ( A — B ) , a multiple of AB by m ; and m ( A + B - C ) , a multiple of the excess of A + B above C , by m . Also , mA and B are equimultiples of A and B by m . The ...
... multiple of A by m . So m ( A + B ) is a multiple of A + B by m ; m ( A — B ) , a multiple of AB by m ; and m ( A + B - C ) , a multiple of the excess of A + B above C , by m . Also , mA and B are equimultiples of A and B by m . The ...
Seite 119
... multiple of D + E + F. " COR . - Hence , if m be any number , mD + mE + mF = m ( D + E + F ) . For mD , mE , and mF are multiples of D , E , and F , by m ; therefore their sum is also a multiple of D + E + F , by m . PROPOSITION II ...
... multiple of D + E + F. " COR . - Hence , if m be any number , mD + mE + mF = m ( D + E + F ) . For mD , mE , and mF are multiples of D , E , and F , by m ; therefore their sum is also a multiple of D + E + F , by m . PROPOSITION II ...
Seite 120
... multiples , taken in the order of the terms , are proportional . to Given that A : B :: C : D , and let m and n be ... multiple of the difference of the two quantities that the whole is of the whole . Given mA and mB any equimultiples ...
... multiples , taken in the order of the terms , are proportional . to Given that A : B :: C : D , and let m and n be ... multiple of the difference of the two quantities that the whole is of the whole . Given mA and mB any equimultiples ...
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Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angles angle ABC angle ACB angle BAC apothem base BC BC is equal bisected centre Chambers's chord circle ABC circumference Const cosec cosine described diameter divided double draw equal angles equal to twice equiangular equilateral equilateral polygon equimultiples exterior angle fore given line given point given straight line gnomon greater hence hypotenuse inscribed isosceles triangle less line drawn multiple number of sides opposite angle parallel parallelogram perimeter perpendicular polygon produced proportional PROPOSITION prove radius ratio rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle segment semiperimeter shewn similar sine square on AC straight line AC tangent THEOREM third touches the circle triangle ABC triangle DEF twice the rectangle vertical angle wherefore
Beliebte Passagen
Seite 23 - 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. either the sides adjacent to the equal...
Seite 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Seite 51 - 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.
Seite 53 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...
Seite 3 - 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.
Seite 29 - 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.
Seite 117 - And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to d ', then, for shortness...
Seite 13 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Seite 159 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Seite 60 - CB, BA, by twice the rectangle CB, BD. Secondly, Let AD fall without the triangle ABC. Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i.