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, 1842 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 48.
Σελίδα 46
... similar 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 ...
... similar 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 ...
Σελίδα 62
... Similar segments of a circle , are those in which the angles are equal , or which contain equal an- gles . PROP . I. PROB . To find the centre of a given circle . C ; Let ABC be the given circle ; it is required to find its centre ...
... Similar segments of a circle , are those in which the angles are equal , or which contain equal an- gles . PROP . I. PROB . To find the centre of a given circle . C ; Let ABC be the given circle ; it is required to find its centre ...
Σελίδα 76
... similar to the segment ADB , and similar segments of circles contain ( 9. def . 3. ) equal angles , the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) . PROP . XXIV . THEOR . A B Similar ...
... similar to the segment ADB , and similar segments of circles contain ( 9. def . 3. ) equal angles , the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) . PROP . XXIV . THEOR . A B Similar ...
Σελίδα 78
... similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
... similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
Σελίδα 87
... similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides ...
... similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides ...
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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 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 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 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 149 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of...
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 9 - 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 52 - 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 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 296 - 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.
Σελίδα 50 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 15 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...