The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 31833 |
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Resultat 1-5 av 37
Side 27
... hypotenuse into two parallelograms . It can be proved , that each of those parallelograms is respectively to the 2 , on that side of the triangle which is adjacent to it . For , if the acute angle contained by that side , and the hypotenuse ...
... hypotenuse into two parallelograms . It can be proved , that each of those parallelograms is respectively to the 2 , on that side of the triangle which is adjacent to it . For , if the acute angle contained by that side , and the hypotenuse ...
Side 36
... hypotenuse , with the right an- gle ( CBA ) is equal to half the hypotenuse . Fig . 8 . ANALYSIS . = Suppose it to be the case . Then since AD is to DB , the angles DBA and DAB are = . Draw DE parallel to BC ; then ( by prop . 6. of ...
... hypotenuse , with the right an- gle ( CBA ) is equal to half the hypotenuse . Fig . 8 . ANALYSIS . = Suppose it to be the case . Then since AD is to DB , the angles DBA and DAB are = . Draw DE parallel to BC ; then ( by prop . 6. of ...
Side 44
... hypotenuse ( BC ) and point ( D ) where perpendicular falls , to construct it . Fig . 23 . ANALYSIS . Suppose BGC to be the required triangle . Bisect BC in E ; join EG ; it is to EB or EC . Therefore , if you raise a perpendicular DG ...
... hypotenuse ( BC ) and point ( D ) where perpendicular falls , to construct it . Fig . 23 . ANALYSIS . Suppose BGC to be the required triangle . Bisect BC in E ; join EG ; it is to EB or EC . Therefore , if you raise a perpendicular DG ...
Side 45
... hypotenuse and perpendicular of a right angled triangle , is equal to the rectangle un- der the sides . Fig . 25 . For , complete the rect . DC under the hypot . and per- pendicular , and also the rect . BF under the sides : then it is ...
... hypotenuse and perpendicular of a right angled triangle , is equal to the rectangle un- der the sides . Fig . 25 . For , complete the rect . DC under the hypot . and per- pendicular , and also the rect . BF under the sides : then it is ...
Side 50
... hypotenuse and side of an isosceles right angled triangle to construct it . Fig . 37 . ANALYSIS . Suppose ACD to be the required triangle ; join CB . Then , because AB is the difference , DB is = to DC ; .. the angle DCB is = to DBC ...
... hypotenuse and side of an isosceles right angled triangle to construct it . Fig . 37 . ANALYSIS . Suppose ACD to be the required triangle ; join CB . Then , because AB is the difference , DB is = to DC ; .. the angle DCB is = to DBC ...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... Euclides Uten tilgangsbegrensning - 1821 |
Vanlige uttrykk og setninger
adjacent altitude ANALYSIS angle contained antecedent assumed bisecting line chord circumference circumscribing circle connecting line construct conterminous dedu diagonal diameter directum divided draw a right drawn line equal angles equiangular equilateral triangle evident external angle extremity given angle given circle given figure given in position given line given point given ratio given right line given triangle half the difference half the given hypotenuse inscribed intercept intersect isosceles triangle less lesser let fall line bisecting lines be drawn magnitude mean proportional meet opposite angle opposite side parallelogram pass perpendicular point of bisection point of contact polygons PROB PROP radii radius rect rectangle required triangle respectively right angled triangle secant segts semicircle side subtending similar square Suppose tangent THEOR triangle ABC vertex vertical angle whole line
Populære avsnitt
Side 100 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 11 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 130 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Side 135 - ... a circle. The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse.
Side 32 - ... polygons are to each other in the duplicate ratio of their homologous sides.
Side 37 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle.
Side 124 - If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle.
Side 6 - Convertendo ; when it is concluded, that, if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Side 10 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other. Let ABC, DEF be two triangles, having the two sides AB, AC, equal to the two sides DE, DF, each to each, viz.
Side 118 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.