Self-examinations in EuclidW. P. Grant, 1829 - 188 sider |
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Side 4
... four - sided figures and polygons may not lie wholly in the same plane . Is any thing superfluous in this definition ? It is sufficient that one of its angles be a right angle . The definition of a square may be amended as follows : A ...
... four - sided figures and polygons may not lie wholly in the same plane . Is any thing superfluous in this definition ? It is sufficient that one of its angles be a right angle . The definition of a square may be amended as follows : A ...
Side 9
... four cases , three of the six angles and sides being equal , the triangles are shewn to be equal and identical in all respects . In all the six sides and angles , taken three and three together , 20 combinations . there are 6.5.4 2.3 ...
... four cases , three of the six angles and sides being equal , the triangles are shewn to be equal and identical in all respects . In all the six sides and angles , taken three and three together , 20 combinations . there are 6.5.4 2.3 ...
Side 15
... four parts ; and so on . PROP . X. 43. The word ' finite ' is here superfluous , since what is ' given ' is necessarily finite . 44. Does this proposition include all possible cases ? If the given point C be at an extremity A , it will ...
... four parts ; and so on . PROP . X. 43. The word ' finite ' is here superfluous , since what is ' given ' is necessarily finite . 44. Does this proposition include all possible cases ? If the given point C be at an extremity A , it will ...
Side 17
... four angles are twice the two angles CEA , AED . But angles CEA , AED together two right angles ; ..the four angles together four right angles . = PROP . XV . COR . 2 . 51. Prove the Corollary . Let the lines AP , BP , CP , & c . all ...
... four angles are twice the two angles CEA , AED . But angles CEA , AED together two right angles ; ..the four angles together four right angles . = PROP . XV . COR . 2 . 51. Prove the Corollary . Let the lines AP , BP , CP , & c . all ...
Side 26
... four of the quadrilateral . S But ( Cor . 1 , Prop . XXXII . ) , the of a quadrilateral = four L3 . ¡ . L ' A , ABD together = two Ls . Hence ( XXVIII . ) , AC || BD . In the same manner it may be shewn that AB CD . .. ACDB is a ...
... four of the quadrilateral . S But ( Cor . 1 , Prop . XXXII . ) , the of a quadrilateral = four L3 . ¡ . L ' A , ABD together = two Ls . Hence ( XXVIII . ) , AC || BD . In the same manner it may be shewn that AB CD . .. ACDB is a ...
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AB² ABCD AC² AD² AE x EB AE² AG² Algebraically Altitude ANALYTICAL GEOMETRY axes axiom base BD² bisect Book XI CB² CD² centre Circumscribing Circumscribing Sphere Co-ordinate Planes compound ratio DE² definition demonstration describe diameter distance Dodecagon draw a touching drawn EF² equilateral equimultiples Euclid Euclid's Elements extremities Geometric Mean Geometrical given ³ given line given point given Sphere Hence inscribed intersection join magnitude meet OP² passing Pentagon plane ABC plane YOX polygon position produced proportionals proposition Propp Prove Q. E. D. PROP quadrilateral quantities Radius regular Decagon right angles segment shew shewn straight line subtended Surface take any point tangent Theorem touch the given Trapezium triangle vertex وو
Populære avsnitt
Side 9 - If two triangles have two sides of the one equal to two sides of the...
Side 18 - Any two sides of a triangle are together greater than the third side.
Side 21 - Geometry, printed anno 1760, observes in his notes, that it ought to have been shewn, that the point F falls below the line EG. This probably Euclid omitted, as it is very easy to perceive, that DG being equal to DF, the point G is in the circumference of a circle described from the centre D at the distance DF, and must be in that part of it which is above the straight line EF, because DG falls above DF, the angle EDG being greater . than the angle EDF.
Side 71 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Side 8 - For, if the triangle ABC be applied to DEF, so that the point A may be on D, and the straight line AB upon DE ; the point B shall coincide with the point E...
Side 9 - Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each.
Side 20 - Of the two sides DE, DF, let DE be the side which is not greater than the other, and at the point D, in the straight line DE, make (i.
Side 49 - The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and of others, that which is nearer to the perpendicular is less than the more remote; and two, and only two, equal straight lines can be drawn from the given point to the given straight line, one on each side of the perpendicular.
Side 24 - Two straight lines which intersect one another cannot be both parallel to the same straight line.
Side 175 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.