The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Side 9
... quadrilateral whose four sides are equal is called a lozenge . xxx . A lozenge which has a right angle is called a square . XXXI . A polygon which has five sides is called a pentagon ; one which has six sides , a hexagon , and so on ...
... quadrilateral whose four sides are equal is called a lozenge . xxx . A lozenge which has a right angle is called a square . XXXI . A polygon which has five sides is called a pentagon ; one which has six sides , a hexagon , and so on ...
Side 19
... quadrilateral be equal , and the diagonal bisects the angle between them , their other sides are equal . 3. If two lines be at right angles , and if each bisect the other , then any point in either is equally distant from the ...
... quadrilateral be equal , and the diagonal bisects the angle between them , their other sides are equal . 3. If two lines be at right angles , and if each bisect the other , then any point in either is equally distant from the ...
Side 33
... quadrilateral be respectively the greatest and least , the angles adjacent to the least are greater than their opposite angles . 4. In any triangle , the perpendicular from the vertex opposite the side which is not less than either of ...
... quadrilateral be respectively the greatest and least , the angles adjacent to the least are greater than their opposite angles . 4. In any triangle , the perpendicular from the vertex opposite the side which is not less than either of ...
Side 36
... quadrilateral is greater than the sum of its diagonals . Def . - A line drawn from any angle of a triangle to the middle point of the opposite side is called a median of the triangle . 9. The sum of the three medians of a triangle is ...
... quadrilateral is greater than the sum of its diagonals . Def . - A line drawn from any angle of a triangle to the middle point of the opposite side is called a median of the triangle . 9. The sum of the three medians of a triangle is ...
Side 44
... at any finite distance , they are said to be PARALLEL . DEF . II - A parallelogram is a quadrilateral , both pairs of whose opposite sides are parallel . DEF . III . - The right line joining either 44 [ BOOK I. THE ELEMENTS OF EUCLID .
... at any finite distance , they are said to be PARALLEL . DEF . II - A parallelogram is a quadrilateral , both pairs of whose opposite sides are parallel . DEF . III . - The right line joining either 44 [ BOOK I. 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.