Self-examinations in EuclidW. P. Grant, 1829 - 188 sider |
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Side iv
... necessary to give . Euclid , although decidedly the most perfect system of reasoning extant , is yet , in many respects , deficient or erroneous . These defects and errors have been explained , and , in most cases , removed . The text ...
... necessary to give . Euclid , although decidedly the most perfect system of reasoning extant , is yet , in many respects , deficient or erroneous . These defects and errors have been explained , and , in most cases , removed . The text ...
Side 2
... necessary as Simson rightly asserts , to consider a Solid , or that which has length , breadth , and thickness . The boundary of a Solid is a superficies having length and breadth , but no thick- ness ; the boundary of a superficies is ...
... necessary as Simson rightly asserts , to consider a Solid , or that which has length , breadth , and thickness . The boundary of a Solid is a superficies having length and breadth , but no thick- ness ; the boundary of a superficies is ...
Side 3
... necessary to bear in mind , that the magnitude of an angle , is quite independent of the length of the straight lines which form it . The angle A , for instance , is greater than the angle B. A pair of compasses will illustrate , very ...
... necessary to bear in mind , that the magnitude of an angle , is quite independent of the length of the straight lines which form it . The angle A , for instance , is greater than the angle B. A pair of compasses will illustrate , very ...
Side 6
... necessary to describe the whole circles ? In practice it will be sufficient to describe merely those parts which intersect ; thus D C. F D A. B 21. Is the construction , when the entire circles are described , sufficient for other ...
... necessary to describe the whole circles ? In practice it will be sufficient to describe merely those parts which intersect ; thus D C. F D A. B 21. Is the construction , when the entire circles are described , sufficient for other ...
Side 7
... necessary condition . At any rate the point A must be given in position , and it must be a condition that AB is greater than C. 6 24. What is meant by given ' as referred to the straight line C ? Since the straight line C does not enter ...
... necessary condition . At any rate the point A must be given in position , and it must be a condition that AB is greater than C. 6 24. What is meant by given ' as referred to the straight line C ? Since the straight line C does not enter ...
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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.