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 43.
Σελίδα 33
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallelo- A 5 OF GEOMETRY . BOOK I. 33 Th. 32.), and the opposite ...
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallelo- A 5 OF GEOMETRY . BOOK I. 33 Th. 32.), and the opposite ...
Σελίδα 34
... ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 34. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is com- mon ; therefore ...
... ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 34. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is com- mon ; therefore ...
Σελίδα 36
... ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ...
... ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ...
Σελίδα 37
... ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD , and are therefore ...
... ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD , and are therefore ...
Σελίδα 39
... ABCD is equal to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , hav- ing the angle FKM equal to the given angle E. COR . From this it is manifest how to a ...
... ABCD is equal to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , hav- ing the angle FKM equal to the given angle E. COR . From this it is manifest how to a ...
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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 described 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 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.