Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson...together with a Selection of Geometrical Exercises from the Senate-house and College Examination Papers .... the first six books, and the portions of the eleventh and twelfth books read at CambridgeLongman, Green, Longman, Roberts, & Green, 1865 - 504 sider |
Fra bogen
Resultater 1-5 af 75
Side 105
... point K , from which to the circumference DEF fall more than two equal straight lines KB , KG , KF ; therefore the ... contact . Let the circle ADE touch the circle ABC'internally in the point Æ ; and let F be the center of the circle ...
... point K , from which to the circumference DEF fall more than two equal straight lines KB , KG , KF ; therefore the ... contact . Let the circle ADE touch the circle ABC'internally in the point Æ ; and let F be the center of the circle ...
Side 106
... point A , that is , it must pass through it . Therefore , if one circle , & c . Q. E.D. PROPOSITION XII . THEOREM . If two circles touch each other externally in any point , the straight line ... point of contact : (. 106 EUCLID'S ELEMENTS .
... point A , that is , it must pass through it . Therefore , if one circle , & c . Q. E.D. PROPOSITION XII . THEOREM . If two circles touch each other externally in any point , the straight line ... point of contact : (. 106 EUCLID'S ELEMENTS .
Side 107
... point of contact : ( III . 11. ) but it does not pass through it , because the points B , D are without the straight line GH ; which is absurd : therefore one circle cannot touch another on the inside in more points : than one . Nor can ...
... point of contact : ( III . 11. ) but it does not pass through it , because the points B , D are without the straight line GH ; which is absurd : therefore one circle cannot touch another on the inside in more points : than one . Nor can ...
Side 111
... point D draw DF at right angles to EA , ( 1. 11. ) meeting the circumference of the circle AFG in F ; and join EBF ... contact , shall be perpendicular to the line touching the circle . Let the straight line DE touch the circle ABC in the ...
... point D draw DF at right angles to EA , ( 1. 11. ) meeting the circumference of the circle AFG in F ; and join EBF ... contact , shall be perpendicular to the line touching the circle . Let the straight line DE touch the circle ABC in the ...
Side 112
... point of contact a straight line be drawn at right angles to the touching line , the center of the circle shall be in that line . Let the straight line DE touch the circle ABC in C , and from Clet CA be drawn at right angles to DE ...
... point of contact a straight line be drawn at right angles to the touching line , the center of the circle shall be in that line . Let the straight line DE touch the circle ABC in C , and from Clet CA be drawn at right angles to DE ...
Andre udgaver - Se alle
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ... Robert Potts Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
A₁ ABCD AC is equal angle ABC angle ACB angle BAC angle equal Apply Euc base BC bisects the angle chord circle ABC circle described circle whose center circles touch circumscribing circle construction describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line greater hypotenuse isosceles triangle Let ABC line joining lines be drawn meet the circumference multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane point of contact polygon produced Prop proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius rectangle contained rectilineal figure right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC vertex vertical angle wherefore
Populære passager
Side 23 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.
Side xiv - The sluggard is wiser in his own conceit than seven men that can render a reason.
Side 6 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Side 29 - 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 71 - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Side 15 - 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 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts 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.
Side 2 - 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 34 - Equal triangles, upon equal bases in the same straight line, and towards the same parts, are between the same parallels. Let the equal triangles ABC, DEF be upon equal bases BC, EF, in the same straight line BF, and towards the same parts.
Side 28 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.