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, 1849 - 317 páginas |
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Página 4
... demonstrating more easily some of the properties of 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 ...
... demonstrating more easily some of the properties of 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 ...
Página 6
... demonstrate it to others when it has been found out . This is either Analytical or Syn- thetical . 16. Analysis , or the Analytic method , is the art or mode of finding out the truth of a proposition , by first supposing the thing to be ...
... demonstrate it to others when it has been found out . This is either Analytical or Syn- thetical . 16. Analysis , or the Analytic method , is the art or mode of finding out the truth of a proposition , by first supposing the thing to be ...
Página 14
... demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG to the part BCF , the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the D F base of the triangle ABC ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG to the part BCF , the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the D F base of the triangle ABC ...
Página 15
... ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; C A B but it has been demonstrated to be greater than it OF GEOMETRY . BOOK I. 15.
... ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; C A B but it has been demonstrated to be greater than it OF GEOMETRY . BOOK I. 15.
Página 16
... demonstrated to be greater than it ; which is impossi ble . E F But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ...
... demonstrated to be greater than it ; which is impossi ble . E F But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ...
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Términos y frases comunes
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 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
Pasajes populares
Página 149 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 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 on the line between the points of section, is equal to the square on half the line.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 283 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 26 - ... sides 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 triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.