Euclid's Elements of GeometryBell & Daldy, 1872 - 261 páginas |
Dentro del libro
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Página 77
... inscribed in a circle , the greatest is the diameter . PART 2. — And of the others , that which is nearer the centre is greater than the line more remote . PART 1. - The diameter AB is greater than any other line ED . For draw CD and CE ...
... inscribed in a circle , the greatest is the diameter . PART 2. — And of the others , that which is nearer the centre is greater than the line more remote . PART 1. - The diameter AB is greater than any other line ED . For draw CD and CE ...
Página 83
... inscribed in a circle , are equal to two right angles . B For , draw AC and FB , and because the angles ACB and AFB are in the same segment AFCB , ACB is equal to AFB ( by Prop . 21. B. 3 ) ; and because the angles ACF and ABF are in ...
... inscribed in a circle , are equal to two right angles . B For , draw AC and FB , and because the angles ACB and AFB are in the same segment AFCB , ACB is equal to AFB ( by Prop . 21. B. 3 ) ; and because the angles ACF and ABF are in ...
Página 145
... inscribed in a circle , when its extremities are in the circumference of the circle . PROPOSITION I. PROBLEM . In a given circle ( BCA ) to inscribe a given right line ( D ) which is not greater than the diameter of the circle . Draw a ...
... inscribed in a circle , when its extremities are in the circumference of the circle . PROPOSITION I. PROBLEM . In a given circle ( BCA ) to inscribe a given right line ( D ) which is not greater than the diameter of the circle . Draw a ...
Página 147
... inscribe a circle in a given triangle ( BAC ) . Bisect any two angles B and C , by the right lines BD and CD , and ... inscribed in the given triangle . For draw DE and DG perpen- dicular to BA and AC ; and since in the triangles DEB ...
... inscribe a circle in a given triangle ( BAC ) . Bisect any two angles B and C , by the right lines BD and CD , and ... inscribed in the given triangle . For draw DE and DG perpen- dicular to BA and AC ; and since in the triangles DEB ...
Página 149
... and therefore the circle passes through D , and is circum- scribed about the quadrilateral figure AFDC . + See First Figure . * See adjoining Figure . See Second Figure . PROPOSITION VI . PROBLEM . To inscribe a square in FOURTH BOOK . 14 .
... and therefore the circle passes through D , and is circum- scribed about the quadrilateral figure AFDC . + See First Figure . * See adjoining Figure . See Second Figure . PROPOSITION VI . PROBLEM . To inscribe a square in FOURTH BOOK . 14 .
Otras ediciones - Ver todas
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington Sin vista previa disponible - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington Sin vista previa disponible - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington Sin vista previa disponible - 2015 |
Términos y frases comunes
absurd AC and CB AC by Prop AC is equal angle ABC angles by Prop arch base bisected centre circumference CKMB co-efficient Const contained in CD contained oftener divided divisor double draw drawn equal angles equal by Constr equal by Hypoth equal by Prop equal to twice equation equi equi-multiples equi-submultiples equiangular equilateral external angle fore four magnitudes proportional given angle given circle given line given right line given triangle gonal half a right inscribed less multiplying oftener contained parallel parallelogram perpendicular PROPOSITION quantities rectangle under AC rectilineal figure remaining angles remaining side right angles right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle
Pasajes populares
Página 18 - If two triangles have two sides of the one equal to two sides of the...
Página 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 207 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Página 216 - 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 127 - In any proportion, the product of the means is equal to the product of the extremes.
Página 161 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Página 112 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Página 213 - ... are to one another in the duplicate ratio of their homologous sides.
Página 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Página 88 - 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.