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 25
Pagina 107
... fourth , equal to it , or less ; then the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth . 6. Magnitudes are said to be proportionals , when the first has the same ratio to the ...
... fourth , equal to it , or less ; then the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth . 6. Magnitudes are said to be proportionals , when the first has the same ratio to the ...
Pagina 108
... fourth ; or that the first is to the third as the second to the fourth : See Prop . 16 . of this Book . 15. Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to the first , as the fourth ...
... fourth ; or that the first is to the third as the second to the fourth : See Prop . 16 . of this Book . 15. Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to the first , as the fourth ...
Pagina 109
... fourth of the first rank , so is the third from the last , to the last but two , of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition . It is demonstrated in the 23d Prop . of ...
... fourth of the first rank , so is the third from the last , to the last but two , of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition . It is demonstrated in the 23d Prop . of ...
Pagina 111
... fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the third ...
... fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the third ...
Pagina 112
... fourth ; the first is to the second as the third to the fourth . First , if mA , mB be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and B equimultiples by any number n ; and of A and B equimultiples by any ...
... fourth ; the first is to the second as the third to the fourth . First , if mA , mB be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and B equimultiples by any number n ; and of A and B equimultiples by any ...
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.