Self-examinations in EuclidW. P. Grant, 1829 - 188 páginas |
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Página 69
... regular polygons , whose number of sides is 7 , 9 , 11 , 13 , 14 , 17 , & c . Gauss , however , has shewn in his Disquisitiones Arith- metica , that any polygon whose number of sides is of the form 2 ′′ + 1 , provided also that this ...
... regular polygons , whose number of sides is 7 , 9 , 11 , 13 , 14 , 17 , & c . Gauss , however , has shewn in his Disquisitiones Arith- metica , that any polygon whose number of sides is of the form 2 ′′ + 1 , provided also that this ...
Página 158
... regular or irregular . 323. Required to draw from a given ( · ) a rectilinear path meeting all the sides of a Polygon , and returning to the ( · ) , such that each pair of its contiguous sides may be equally inclined to a side or side ...
... regular or irregular . 323. Required to draw from a given ( · ) a rectilinear path meeting all the sides of a Polygon , and returning to the ( · ) , such that each pair of its contiguous sides may be equally inclined to a side or side ...
Página 161
... regular Pentagon are = , and they will cut each other in mean and extreme Ratio . The first is evident . The second is proved by Propp . XXVIII . , Book III .; XXVII . , Book III .; XXVII . , Book I .; XXXIV . , Book I .; V. , Book I ...
... regular Pentagon are = , and they will cut each other in mean and extreme Ratio . The first is evident . The second is proved by Propp . XXVIII . , Book III .; XXVII . , Book III .; XXVII . , Book I .; XXXIV . , Book I .; V. , Book I ...
Página 176
... regular Pentagon , a regular Hexagon , and a regular Decagon be inscribed in the same , ( the side of the Pentagon ) 2 ( side of the Hexagon ) 2 + ( side of the Deca- gon ) .- Euc . , Book XIII . , Prop . X. = 411. If the Semi ...
... regular Pentagon , a regular Hexagon , and a regular Decagon be inscribed in the same , ( the side of the Pentagon ) 2 ( side of the Hexagon ) 2 + ( side of the Deca- gon ) .- Euc . , Book XIII . , Prop . X. = 411. If the Semi ...
Página 177
... regular bodies.— Euc . , Book XIII . , Prop . XVII . , Schol . 419. Only three kinds of regular plane figures can fill up the plane space about a ( · ) ; viz . six △ 3 , four , and three regular Hexagons . Why do bees , in the ...
... regular bodies.— Euc . , Book XIII . , Prop . XVII . , Schol . 419. Only three kinds of regular plane figures can fill up the plane space about a ( · ) ; viz . six △ 3 , four , and three regular Hexagons . Why do bees , in the ...
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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.