Self-examinations in EuclidW. P. Grant, 1829 - 188 páginas |
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Página 9
... opposite to equal angles : in each of which 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 ...
... opposite to equal angles : in each of which 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 ...
Página 23
... opposite sides of it . 69 . angles ? Are the angles AEF , EFD the only two alternate ' The angles BEF , EFC are alternate . 70. If alternate L AEF = alternate EFD , does it necessarily follow that the other two alternate angles are ...
... opposite sides of it . 69 . angles ? Are the angles AEF , EFD the only two alternate ' The angles BEF , EFC are alternate . 70. If alternate L AEF = alternate EFD , does it necessarily follow that the other two alternate angles are ...
Página 24
... opposite angle , the straight lines are parallel ; and then because the two interior angles are together equal to two right angles that the straight lines are parallel . PROP . XXIX . 72. This proposition , which is the converse of Prop ...
... opposite angle , the straight lines are parallel ; and then because the two interior angles are together equal to two right angles that the straight lines are parallel . PROP . XXIX . 72. This proposition , which is the converse of Prop ...
Página 25
... opposite L3 . 77. Prove the converse of this Proposition , viz . first , that if in any quadrilateral the opposite sides are = , it is a it is a . Let ABCD be a quadrilateral having the side AC side BD , and side AB = side CD ; it is a ...
... opposite L3 . 77. Prove the converse of this Proposition , viz . first , that if in any quadrilateral the opposite sides are = , it is a it is a . Let ABCD be a quadrilateral having the side AC side BD , and side AB = side CD ; it is a ...
Página 26
... opposite Ls are equal , it is a . The figure being the same as in the first case , let LA = LD , : . and ABD = L ACD ; then ABCD is a . :: L A = L D , LABDL ACD . = .. LA , ABD together D , ACD together . ..twice the A , ABD = the four ...
... opposite Ls are equal , it is a . The figure being the same as in the first case , let LA = LD , : . and ABD = L ACD ; then ABCD is a . :: L A = L D , LABDL ACD . = .. LA , ABD together D , ACD together . ..twice the A , ABD = the four ...
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Términos y frases comunes
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
Pasajes populares
Página 9 - If two triangles have two sides of the one equal to two sides of the...
Página 18 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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.
Página 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...
Página 9 - Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each.
Página 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.
Página 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.
Página 24 - Two straight lines which intersect one another cannot be both parallel to the same straight line.
Página 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.