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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 σελίδες |
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Αποτελέσματα 1 - 5 από τα 36.
Σελίδα 17
... construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB ...
... construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB ...
Σελίδα 37
... construction will apply to the problem : to make a triangle equivalent to a given rectangle . PROP . XLIII . THEOR . The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another ...
... construction will apply to the problem : to make a triangle equivalent to a given rectangle . PROP . XLIII . THEOR . The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another ...
Σελίδα 45
... construction will apply : for , mak- ing BCA equal to the given angle , and AC equal to the adjacent side ; then , from A as centre , with a radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB ...
... construction will apply : for , mak- ing BCA equal to the given angle , and AC equal to the adjacent side ; then , from A as centre , with a radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB ...
Σελίδα 46
... construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square equivalent to the difference of two given squares . Draw , as in ...
... construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square equivalent to the difference of two given squares . Draw , as in ...
Σελίδα 64
... construction being made , because the radii EA , FB are equal to one another , the angle EAF is equal ( 5. 1. ) to the angle EBF ; and the right angle AFE is equal to the right angle BFE : Therefore , in the two triangles EAF , EBF ...
... construction being made , because the radii EA , FB are equal to one another , the angle EAF is equal ( 5. 1. ) to the angle EBF ; and the right angle AFE is equal to the right angle BFE : Therefore , in the two triangles EAF , EBF ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition 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 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 51 - 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 29 - 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 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Σελίδα 11 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Σελίδα 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 84 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 80 - 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 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.