The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Resultat 1-5 av 32
Side 106
... touch a circle when it meets the circle , and , being produced both ways , does not cut it ; the line is called a tangent to the circle , and the point where it touches it the point of contact . In Modern Geometry a curve is considered ...
... touch a circle when it meets the circle , and , being produced both ways , does not cut it ; the line is called a tangent to the circle , and the point where it touches it the point of contact . In Modern Geometry a curve is considered ...
Side 107
... touch one another when they meet , but do not intersect . There are two species of contact : - 1. When each circle is external to the other . 2. When one is inside the other . The following is the modern definition of curve - contact ...
... touch one another when they meet , but do not intersect . There are two species of contact : - 1. When each circle is external to the other . 2. When one is inside the other . The following is the modern definition of curve - contact ...
Side 113
... touch another circle ( ADE ) internally in any point ( A ) , it is not concentric with it . Dem . If possible let the circles be concentric , and let O be the centre of each . Join OA , and draw any other line OD , cutting the circles ...
... touch another circle ( ADE ) internally in any point ( A ) , it is not concentric with it . Dem . If possible let the circles be concentric , and let O be the centre of each . Join OA , and draw any other line OD , cutting the circles ...
Side 119
... touch another circle ( APB ) in- ternally at any point P , the line joining the centres must pass through that point . Dem . - Let O be the centre of APB . Join OP . I say the centre of the smaller circle is in the line OP . If not ...
... touch another circle ( APB ) in- ternally at any point P , the line joining the centres must pass through that point . Dem . - Let O be the centre of APB . Join OP . I say the centre of the smaller circle is in the line OP . If not ...
Side 120
... touch each other at any point , the centres and that point are collinear . " And this latter Proposition is a limiting case of the theorem given in Pro- position III . , Cor . 4 , that " The line joining the centres of two intersecting ...
... touch each other at any point , the centres and that point are collinear . " And this latter Proposition is a limiting case of the theorem given in Pro- position III . , Cor . 4 , that " The line joining the centres of two intersecting ...
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.