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 GeometryJ.B. Lippincott & Company, 1860 - 317 sider |
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Resultat 1-5 av 31
Side 61
... tangent , and the point in com- mon , the point of contact . 2. Circles are said to touch one another , which meet , but do not cut one another . 3. Straight lines are said to be equally dis- tant from the centre of a circle , when the ...
... tangent , and the point in com- mon , the point of contact . 2. Circles are said to touch one another , which meet , but do not cut one another . 3. Straight lines are said to be equally dis- tant from the centre of a circle , when the ...
Side 72
... tangent to a circle is perpendicular to the diameter drawn from the point of contact . COR . 3. It follows , likewise , that tangents at each extremity of the diameter are parallel ( Cor . 28. B. 1. ) ; and , conversely , parallel ...
... tangent to a circle is perpendicular to the diameter drawn from the point of contact . COR . 3. It follows , likewise , that tangents at each extremity of the diameter are parallel ( Cor . 28. B. 1. ) ; and , conversely , parallel ...
Side 73
... tangents passing through the point A. For , by producing the tangent FD till it meets the circumference AG , and joining E and the poin of intersection , and also A and the point where this last line will intersect the circumference DC ...
... tangents passing through the point A. For , by producing the tangent FD till it meets the circumference AG , and joining E and the poin of intersection , and also A and the point where this last line will intersect the circumference DC ...
Side 85
... tangent , it follows that the angle included by two tangents , drawn from the same point , is bisected by a line drawn from the centre of the circle to that point ; for this line forms the hypotenuse common to two equal right angled ...
... tangent , it follows that the angle included by two tangents , drawn from the same point , is bisected by a line drawn from the centre of the circle to that point ; for this line forms the hypotenuse common to two equal right angled ...
Side 89
... tangents to the circle , as AB , CD ; then , each A of the arcs intercepted is a semi - cir- cumference , as their ... tangent , the other a chord , which being perpendicular to FE , the arc GEH is bisected by FE ( Cor . 4. Prop . D ...
... tangents to the circle , as AB , CD ; then , each A of the arcs intercepted is a semi - cir- cumference , as their ... tangent , the other a chord , which being perpendicular to FE , the arc GEH is bisected by FE ( Cor . 4. Prop . D ...
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 - 1837 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle BCD 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 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 49 - 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 9 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 27 - 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 17 - 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 13 - 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.
Side 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.
Side 55 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Side 24 - ... 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.
Side 125 - 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 78 - 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.