The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Σελίδα 9
... square . XXXI . A polygon which has five sides is called a pentagon ; one which has six sides , a hexagon , and so on . THE CIRCLE . XXXII . A circle is a plane figure formed by a curved line called the circumference , and is such that ...
... square . XXXI . A polygon which has five sides is called a pentagon ; one which has six sides , a hexagon , and so on . THE CIRCLE . XXXII . A circle is a plane figure formed by a curved line called the circumference , and is such that ...
Σελίδα 49
... square in a given equilateral triangle , having its base on a given side of the triangle . 5. Draw a line parallel to the base of a triangle so that it may be - 1 . equal to the intercept it makes on one of the sides from the extremity ...
... square in a given equilateral triangle , having its base on a given side of the triangle . 5. Draw a line parallel to the base of a triangle so that it may be - 1 . equal to the intercept it makes on one of the sides from the extremity ...
Σελίδα 65
... square . Ꭰ C Sol . - Erect AD at right angles to AB [ x1 . ] , and make it equal to AB [ . ] . Through D draw DC parallel to AB [ xxxi . ] , and through B draw BC parallel to AD ; then AC is the square required . Dem . - Because AC is ...
... square . Ꭰ C Sol . - Erect AD at right angles to AB [ x1 . ] , and make it equal to AB [ . ] . Through D draw DC parallel to AB [ xxxi . ] , and through B draw BC parallel to AD ; then AC is the square required . Dem . - Because AC is ...
Σελίδα 66
... square are squares . 3. If on the four sides of a square , or on the sides produced , points be taken equidistant from the four angles , they will be the angular points of another square , and similarly for a regular pentagon , hexagon ...
... square are squares . 3. If on the four sides of a square , or on the sides produced , points be taken equidistant from the four angles , they will be the angular points of another square , and similarly for a regular pentagon , hexagon ...
Σελίδα 67
... square AF is equal to the sum of the two squares AH and BD . = G F Or thus : Let all the squares be made in reversed directions . Join CG , BK , and through C draw OL parallel to AG . Now , taking the BAC from the right / s BAG , CAK ...
... square AF is equal to the sum of the two squares AH and BD . = G F Or thus : Let all the squares be made in reversed directions . Join CG , BK , and through C draw OL parallel to AG . Now , taking the BAC from the right / s BAG , CAK ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Σελίδα 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...
Σελίδα 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.