Self-examinations in EuclidW. P. Grant, 1829 - 188 sider |
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Side 19
... diameter , the circle HKL would not cut the circle FKD , and consequently no triangle such as FKG could be constructed . If FG , GK were together equal to FK , then the points of intersection K , L would merge into one , and the △ FKG ...
... diameter , the circle HKL would not cut the circle FKD , and consequently no triangle such as FKG could be constructed . If FG , GK were together equal to FK , then the points of intersection K , L would merge into one , and the △ FKG ...
Side 51
... . 132. Euclid has demonstrated the Proposition for those | only which are on the same side of the diameter AD ; is it also true , when they are on different sides ? Let FK be more remote from the Make FHFG , IN BOOK III . 51.
... . 132. Euclid has demonstrated the Proposition for those | only which are on the same side of the diameter AD ; is it also true , when they are on different sides ? Let FK be more remote from the Make FHFG , IN BOOK III . 51.
Side 52
... diameter than FG . HED = △ GED , FH is equally remote with FG . Hence , as in Euclid , FH is less than FK , & c . PROP . VIII . 133. Which is the longest | that can be drawn from any point without the Oce of a to that portion which is ...
... diameter than FG . HED = △ GED , FH is equally remote with FG . Hence , as in Euclid , FH is less than FK , & c . PROP . VIII . 133. Which is the longest | that can be drawn from any point without the Oce of a to that portion which is ...
Side 53
... diameter AB at its extremity A , AC touches the O in A. For in AC take any point E , join DE , intersecting the " in F. Then , DAE is a L the LADE , DEA are together a L. .. the ..the B D AED is < than L. AED is < the L DAE . ..side DE ...
... diameter AB at its extremity A , AC touches the O in A. For in AC take any point E , join DE , intersecting the " in F. Then , DAE is a L the LADE , DEA are together a L. .. the ..the B D AED is < than L. AED is < the L DAE . ..side DE ...
Side 55
... diameter which passes through the point , By an Ex Absurdo it would be easy to shew that not more than two can thus be drawn . PROP . XX . 142. In this Proposition Euclid has supposed two cases , viz . those in which E is first within ...
... diameter which passes through the point , By an Ex Absurdo it would be easy to shew that not more than two can thus be drawn . PROP . XX . 142. In this Proposition Euclid has supposed two cases , viz . those in which E is first within ...
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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.