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 10.
Σελίδα 26
... sides adjacent to the equal angles , or the sides opposite to the equal angles in each ; then shall the other side be equal , each to each ; and also the third angle of the one to the third angle of the other . Let ABC , DEF be two ...
... sides adjacent to the equal angles , or the sides opposite to the equal angles in each ; then shall the other side be equal , each to each ; and also the third angle of the one to the third angle of the other . Let ABC , DEF be two ...
Σελίδα 33
... angles being mutually equal , each pair of adja- cent angles must be equal to two right angles ; therefore , the opposite sides must be equal and parallel . PROP . XXXIV . THEOR . The opposite sides and angles of a parallelogram are ...
... angles being mutually equal , each pair of adja- cent angles must be equal to two right angles ; therefore , the opposite sides must be equal and parallel . PROP . XXXIV . THEOR . The opposite sides and angles of a parallelogram are ...
Σελίδα 100
... Geometry of Solids : to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. " times the angle BAD . But the three angles ABD , ADB , BAD are equal to two right angles , therefore five times the angle BAD is equal ...
... Geometry of Solids : to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. " times the angle BAD . But the three angles ABD , ADB , BAD are equal to two right angles , therefore five times the angle BAD is equal ...
Σελίδα 124
... angle ACE is equal to the alternate angle CAD ( 29. 1. ) : But CAD , by the hypothesis , is equal to the angle BAD ; wherefore BAD is equal to the angle ACE . Again , because the straight line BAE meets the parallels AD , EC , the ...
... angle ACE is equal to the alternate angle CAD ( 29. 1. ) : But CAD , by the hypothesis , is equal to the angle BAD ; wherefore BAD is equal to the angle ACE . Again , because the straight line BAE meets the parallels AD , EC , the ...
Σελίδα 125
... equal to the alternate angle CAD ( 29. 1. ) : But CAD is equal to the angle DAE ( Hyp . ) : therefore also DAE is ... angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are ...
... equal to the alternate angle CAD ( 29. 1. ) : But CAD is equal to the angle DAE ( Hyp . ) : therefore also DAE is ... angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are ...
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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 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 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 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...