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 |
Inni boken
Resultat 1-5 av 47
Side 14
... adjacent internal , are to two right angles ; this internal , with either of the other internal angles , are less than two right angles . Thus any two angles of a triangle can be proved less than two right angles . Cor . 1. If any angle ...
... adjacent internal , are to two right angles ; this internal , with either of the other internal angles , are less than two right angles . Thus any two angles of a triangle can be proved less than two right angles . Cor . 1. If any angle ...
Side 17
... adjacent or opposite to these equal angles , the remaining sides and angles are respectively equal . angles in First , let the sides be adjacent to the each , the sides opposite to either of the angles shall be ; for if not , cut off ...
... adjacent or opposite to these equal angles , the remaining sides and angles are respectively equal . angles in First , let the sides be adjacent to the each , the sides opposite to either of the angles shall be ; for if not , cut off ...
Side 19
... adjacent internal with the other internal , also to two right angles . ... & c . PROP . 29 , THEOR . If a right line intersect two parallel right lines , it makes the alternate angles equal ; and the external angle equal to the internal ...
... adjacent internal with the other internal , also to two right angles . ... & c . PROP . 29 , THEOR . If a right line intersect two parallel right lines , it makes the alternate angles equal ; and the external angle equal to the internal ...
Side 20
... adjacent internal angle ; ) it di- vides the external angle into two parts respectively = to the internal and remote angles , ( by the 29th , ) there- fore , & c . And since the external angle is to the two internal and remote angles ...
... adjacent internal angle ; ) it di- vides the external angle into two parts respectively = to the internal and remote angles , ( by the 29th , ) there- fore , & c . And since the external angle is to the two internal and remote angles ...
Side 21
... adjacent ones ; then the figure will be divided into as many trian- gles as it has sides - 2 ; and the angles of each of the trian- gles into which it is divided are to 2 right angles , & c . Cor . 7. The external angles of any ...
... adjacent ones ; then the figure will be divided into as many trian- gles as it has sides - 2 ; and the angles of each of the trian- gles into which it is divided are to 2 right angles , & c . Cor . 7. The external angles of any ...
Andre utgaver - Vis alle
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.