The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
Inni boken
Resultat 1-5 av 11
Side 269
... NORMAL to it . Cor . 1. - The normal is the least line that may be drawn from a given point to a given plane ; and of all others that may be drawn to it , the lines of any system making equal angles with the normal are equal to each ...
... NORMAL to it . Cor . 1. - The normal is the least line that may be drawn from a given point to a given plane ; and of all others that may be drawn to it , the lines of any system making equal angles with the normal are equal to each ...
Side 270
... normal to X , the angle ABE is right . Therefore AE2 = AB2 + BE2 = AB + BD2 + DE ; because the angle BDE is right . But AB2 + BD2 = AD2 , because the angle ABD is right . Hence AE2 = AD2 + DE2 . Therefore the angle ADE is right B [ I ...
... normal to X , the angle ABE is right . Therefore AE2 = AB2 + BE2 = AB + BD2 + DE ; because the angle BDE is right . But AB2 + BD2 = AD2 , because the angle ABD is right . Hence AE2 = AD2 + DE2 . Therefore the angle ADE is right B [ I ...
Side 271
... normal to the other plane is perpendicular to the line of intersec- tion of the planes . PROP . VII . - THEOREM ... normal to a plane ( X ) , the other line ( CD ) shall be normal to the same plane . Dem . - Let AB , CD meet the plane X ...
... normal to the other plane is perpendicular to the line of intersec- tion of the planes . PROP . VII . - THEOREM ... normal to a plane ( X ) , the other line ( CD ) shall be normal to the same plane . Dem . - Let AB , CD meet the plane X ...
Side 273
... normal to the plane HGK . Hence , since AB and CD are normals to the same plane , they are parallel to one another . PROP . X. - THEOREM . If two intersecting right lines ( AB , BC ) be respectively parallel to two other intersecting ...
... normal to the plane HGK . Hence , since AB and CD are normals to the same plane , they are parallel to one another . PROP . X. - THEOREM . If two intersecting right lines ( AB , BC ) be respectively parallel to two other intersecting ...
Side 276
... normals to these planes . 2. If a line be parallel to each of two planes , the sections which any plane passing through it makes with them are parallel . 3. If a line be parallel to each of two intersecting planes , it is parallel to ...
... normals to these planes . 2. If a line be parallel to each of two planes , the sections which any plane passing through it makes with them are parallel . 3. If a line be parallel to each of two intersecting planes , it is parallel to ...
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.