Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Appendix by Thos. Kirkland. the first six booksA. Miller & Company, 1876 - 403 sider |
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Side 315
... parallelopiped is a solid figure contained by six quadrilateral figures , whereof every opposite two are parallel . PROPOSITION I. THEOREM . One part of a straight line cannot be in a plane , and another part above it . If it be ...
... parallelopiped is a solid figure contained by six quadrilateral figures , whereof every opposite two are parallel . PROPOSITION I. THEOREM . One part of a straight line cannot be in a plane , and another part above it . If it be ...
Side 332
... parallelopiped may be said to be contained by any three of the straight lines which contain the three right angles by which any one of the solid angles of the figure is formed ; or more briefly , by the three adjacent edges of the ...
... parallelopiped may be said to be contained by any three of the straight lines which contain the three right angles by which any one of the solid angles of the figure is formed ; or more briefly , by the three adjacent edges of the ...
Side 333
... parallelopiped would contain abc cubic units , and the product abc would be a proper representation of the volume of the parallelopiped . If the three sides of the figure were equal to one another , or b and c each equal to a , the ...
... parallelopiped would contain abc cubic units , and the product abc would be a proper representation of the volume of the parallelopiped . If the three sides of the figure were equal to one another , or b and c each equal to a , the ...
Side 334
... parallelopiped and the cube have the same relation to each other as the rectangle and the square ? 21. What is the length of an edge of a cube whose volume shall be double that of another cube whose edge is known ? 22. If a straight ...
... parallelopiped and the cube have the same relation to each other as the rectangle and the square ? 21. What is the length of an edge of a cube whose volume shall be double that of another cube whose edge is known ? 22. If a straight ...
Side 335
... parallelopiped which can be made , 30. Shew how to bisect a parallelopiped , so that the area of the section may be the greatest possible . 31. There are two cylinders of equal altitudes , but the base of one of them is three times that ...
... parallelopiped which can be made , 30. Shew how to bisect a parallelopiped , so that the area of the section may be the greatest possible . 31. There are two cylinders of equal altitudes , but the base of one of them is three times that ...
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Almindelige termer og sætninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane polygon produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC twice the rectangle vertex vertical angle wherefore
Populære passager
Side 93 - If a straight line be bisected and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected, and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D ; The squares on AD and DB shall be together double of the squares on AC and CD. CONSTRUCTION. — From the point C draw CE at right angles to AB, and make it equal...
Side 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 145 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Side 88 - If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Side 36 - 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 144 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 92 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Side xv - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.