Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Elements of Plane and Spherical TrigonometryW. E. Dean, 1847 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 98.
Σελίδα 4
... parallel lines . In the third Book , the re- marks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the elements of the science ...
... parallel lines . In the third Book , the re- marks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the elements of the science ...
Σελίδα 6
... parallel lines ) , is the sign of equality ; thus , A = B , implies that the quantity denoted by A is equal to the quantity denoted by B , and is read A equal to B. 19. To signify that A is greater than B , the expression A7 B is used ...
... parallel lines ) , is the sign of equality ; thus , A = B , implies that the quantity denoted by A is equal to the quantity denoted by B , and is read A equal to B. 19. To signify that A is greater than B , the expression A7 B is used ...
Σελίδα 11
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2 ...
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2 ...
Σελίδα 27
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
Σελίδα 28
... parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
... parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 53 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 18 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 54 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 82 - 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.
Σελίδα 31 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Σελίδα 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Σελίδα 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 298 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.