Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 páginas |
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Página xviii
... greater ratio than that of 3 to 1 : therefore the ratio of the circumference to its diameter must be between these two ratios . But that which has rendered him most famous in the eyes of posterity is the fabrication of such admirable ...
... greater ratio than that of 3 to 1 : therefore the ratio of the circumference to its diameter must be between these two ratios . But that which has rendered him most famous in the eyes of posterity is the fabrication of such admirable ...
Página xx
... great number of books , which were considered by the ancients as affording the most perfect examples of the higher ... Ratio , or Proportional Section ; two books . 2. The Section of a Space , in two books . 3. Determinate Section , in ...
... great number of books , which were considered by the ancients as affording the most perfect examples of the higher ... Ratio , or Proportional Section ; two books . 2. The Section of a Space , in two books . 3. Determinate Section , in ...
Página 115
... greater , when the less measures the greater . 2. A multiple is a greater magnitude of a less , when the less measures the greater . 3. Ratio is a certain mutual habitude or relation of two magnitudes of the same kind , according to ...
... greater , when the less measures the greater . 2. A multiple is a greater magnitude of a less , when the less measures the greater . 3. Ratio is a certain mutual habitude or relation of two magnitudes of the same kind , according to ...
Página 116
... greater ratio than the third has to the fourth . " " 4. If the first of four magnitudes be less , when compared to the second , than the third is when compared to the fourth , the first is said to have to the second a less ratio than ...
... greater ratio than the third has to the fourth . " " 4. If the first of four magnitudes be less , when compared to the second , than the third is when compared to the fourth , the first is said to have to the second a less ratio than ...
Página 117
... greater ratio to the second , than the third has to the fourth . + 8. Proportion is a similitude of ratios . 9. Proportion consists of three terms at least . 10. If three magnitudes be proportionals , the first is said to have to the ...
... greater ratio to the second , than the third has to the fourth . + 8. Proportion is a similitude of ratios . 9. Proportion consists of three terms at least . 10. If three magnitudes be proportionals , the first is said to have to the ...
Otras ediciones - Ver todas
Elements of Geometry; Containing the First Six Books of Euclid ... Euclid,John Playfair Vista completa - 1814 |
Términos y frases comunes
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circum circumference BC diameter double draw equal angles equal circles equal right lines equal to F equi equiangular equimultiples Euclid EUCLID'S ELEMENTS exceed exterior angle fore four magnitudes fourth Geometry given circle given point given right line gnomon greater ratio hence inscribed join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deduction Q. E. D. PROPOSITION rectangle contained remaining angle right angles right line AB right line AC sector HEF segment side BC similar and similarly square of AC subtending THEOREM tiple touches the circle triangle ABC triangle DEF whence whole
Pasajes populares
Página xxvi - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Página 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 148 - 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 27 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Página 8 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Página 73 - DH; (I. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Página 99 - To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. . Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, • 17.3. C, D, draw...
Página 7 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Página 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.