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, 1847 - 317 sider |
Inni boken
Resultat 1-5 av 100
Side 9
... Spherical Trigonometry John Playfair. ' BD , is named the angle ABD , or DBA ; and that which is contained by ' BD , CB , is called the angle DBC , or CBD ; but , if there be only one an- ' gle at a point , it may be expressed by a ...
... Spherical Trigonometry John Playfair. ' BD , is named the angle ABD , or DBA ; and that which is contained by ' BD , CB , is called the angle DBC , or CBD ; but , if there be only one an- ' gle at a point , it may be expressed by a ...
Side 14
... Spherical Trigonometry John Playfair. coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the ...
... Spherical Trigonometry John Playfair. coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the ...
Side 15
... Spherical Trigonometry John Playfair. base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral ...
... Spherical Trigonometry John Playfair. base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral ...
Side 16
... Spherical Trigonometry John Playfair. but it has been demonstrated to be greater than it ; which is impossi ble ... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the ...
... Spherical Trigonometry John Playfair. but it has been demonstrated to be greater than it ; which is impossi ble ... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the ...
Side 17
... Spherical Trigonometry John Playfair. tion , as EG and FG ; then , upon the same base EF , and upon the same side of ... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ...
... Spherical Trigonometry John Playfair. tion , as EG and FG ; then , upon the same base EF , and upon the same side of ... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1839 |
Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1856 |
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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...
Side 54 - 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.
Side 82 - 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 31 - 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.
Side 11 - 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.
Side 21 - 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 shall either be two right angles, or shall together be equal to two right angles. For...
Side 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Side 298 - 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.