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, 1837 - 318 sider |
Inni boken
Resultat 6-10 av 92
Side 20
... produced , the exterior angle is greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles ...
... produced , the exterior angle is greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles ...
Side 21
... Produce BC to D ; and because ACD is the exterior angle of the tri- angle ABC , ACD is greater ( 16. 1. ) than the interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than ...
... Produce BC to D ; and because ACD is the exterior angle of the tri- angle ABC , ACD is greater ( 16. 1. ) than the interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than ...
Side 22
... Produce BA to the point D , and make ( 3. 1. ) AD equal to AC ; and join DC . D A Because DA is equal to AC , the an ... producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ; therefore BC ...
... Produce BA to the point D , and make ( 3. 1. ) AD equal to AC ; and join DC . D A Because DA is equal to AC , the an ... producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ; therefore BC ...
Side 23
... Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are greater than the third side , the two sides BA , AE of the triangle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are greater than BE ...
... Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are greater than the third side , the two sides BA , AE of the triangle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are greater than BE ...
Side 27
... produced shall meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) than the interior and opposite ...
... produced shall meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) than the interior and opposite ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |
Vanlige uttrykk og setninger
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 spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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.
Side 12 - AB; but things which are equal to the same are equal to one another...
Side 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.
Side 288 - 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.
Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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 this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.
Side 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Side 127 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side 19 - 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 are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.