The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Side 10
... magnitudes are equal . VIII . Magnitudes that can be made to coincide are equal . The placing of one geometrical magnitude on another , such 10 [ BOOK I. THE ELEMENTS OF EUCLID .
... magnitudes are equal . VIII . Magnitudes that can be made to coincide are equal . The placing of one geometrical magnitude on another , such 10 [ BOOK I. THE ELEMENTS OF EUCLID .
Side 180
... 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 . III . Ratio is the mutual relation of two magnitudes 180 [ BOOK V ...
... 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 . III . Ratio is the mutual relation of two magnitudes 180 [ BOOK V ...
Side 181
Euclides John Casey. III . Ratio is the mutual relation of two magnitudes of the same kind with respect to quantity . IV . Magnitudes are said to have a ratio to one another when the less can be multiplied so as to exceed the greater ...
Euclides John Casey. III . Ratio is the mutual relation of two magnitudes of the same kind with respect to quantity . IV . Magnitudes are said to have a ratio to one another when the less can be multiplied so as to exceed the greater ...
Side 182
... magnitudes is the same as the ratio of the numerical quantities which denote these magnitudes . Thus , the ratio of two commensurable lines is the ratio of the numbers which ex- press their lengths , measured with the same unit . And ...
... magnitudes is the same as the ratio of the numerical quantities which denote these magnitudes . Thus , the ratio of two commensurable lines is the ratio of the numbers which ex- press their lengths , measured with the same unit . And ...
Side 183
... the products 20 , 28 are called equimultiples of 5 and 7 . In like manner 10 and 15 are equimultiples of 2 and 3 , and 18 and 30 of 3 and 5 , & c . v . The first of four magnitudes has to the BOOK V. ] 183 THE ELEMENTS OF EUCLID .
... the products 20 , 28 are called equimultiples of 5 and 7 . In like manner 10 and 15 are equimultiples of 2 and 3 , and 18 and 30 of 3 and 5 , & c . v . The first of four magnitudes has to the BOOK V. ] 183 THE ELEMENTS OF EUCLID .
Vanlige uttrykk og setninger
ABCD AC is equal AD² adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector bisects centre chord circles touch circumference circumscribed circle collinear concurrent lines const coplanar cyclic quadrilateral Dem.-Let diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle Geometry given circle given line given point greater Hence the angle hypotenuse inscribed isosceles less line AC line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped perpendicular plane points of intersection prism PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar square on AC tangent theorem triangle ABC vertex vertical angle
Populære avsnitt
Side 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Side 182 - When of the equimultiples of four magnitudes (taken as in the fifth definition) 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 fourth...
Side 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 102 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 122 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Side 226 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Side 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 63 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 126 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Side 194 - If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.