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, 1853 - 317 pagine |
Dall'interno del libro
Risultati 1-5 di 70
Pagina 12
... the remainder ( 3 . K H D E G F Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal B to the same are equal to one another ; therefore 12 ELEMENTS.
... the remainder ( 3 . K H D E G F Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal B to the same are equal to one another ; therefore 12 ELEMENTS.
Pagina 22
... shewn that B A it is not equal to AB ; therefore AC is greater than AB . PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater than ...
... shewn that B A it is not equal to AB ; therefore AC is greater than AB . PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater than ...
Pagina 23
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC great- er than BD , DC . B D A E Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exte- rior angle ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC great- er than BD , DC . B D A E Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exte- rior angle ...
Pagina 25
... shewn that it is not equal to it : therefore the angle BAC is greater than the angle EDF . B AA F " PROP . XXVI . THEOR . If two triangles 4 . OF GEOMETRY . BOOK I. 25 DF; but the angle BAC greater than the angle ...
... shewn that it is not equal to it : therefore the angle BAC is greater than the angle EDF . B AA F " PROP . XXVI . THEOR . If two triangles 4 . OF GEOMETRY . BOOK I. 25 DF; but the angle BAC greater than the angle ...
Pagina 29
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alter- nate angles ; therefore AB is parallel ( 27. 1. ) to CD . E PROP . XXXI . PROB . G B H -F K D Te draw a straight line through ...
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alter- nate angles ; therefore AB is parallel ( 27. 1. ) to CD . E PROP . XXXI . PROB . G B H -F K D Te draw a straight line through ...
Altre edizioni - Visualizza tutto
Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Visualizzazione completa - 1851 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Visualizzazione completa - 1857 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Visualizzazione completa - 1836 |
Parole e frasi comuni
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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Brani popolari
Pagina 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.
Pagina 74 - THE angles in the same segment of a circle are equal to one another...
Pagina 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Pagina 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.
Pagina 29 - 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 ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Pagina 147 - 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.
Pagina 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Pagina 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Pagina 294 - 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.
Pagina 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.