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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Side 6
... meet with . Trinity College , Sept. 7 , 1833 . * In a book entitled , Memoirs of the Analytic Society , published at Cam- bridge in 1813 , after proving the 47th of Euclid's first book by the theory of functions , the following remark ...
... meet with . Trinity College , Sept. 7 , 1833 . * In a book entitled , Memoirs of the Analytic Society , published at Cam- bridge in 1813 , after proving the 47th of Euclid's first book by the theory of functions , the following remark ...
Side 8
... meet the leg of the equilateral triangle , produced through the connected point ; with the vertex of equilat . tri . as centre , and whole produced leg as radius , describe another circle to meet the other leg pro- duced through the ...
... meet the leg of the equilateral triangle , produced through the connected point ; with the vertex of equilat . tri . as centre , and whole produced leg as radius , describe another circle to meet the other leg pro- duced through the ...
Side 15
... meet one of the sides , then the whole produced line is less than the uncut side and conterminous segment of cut side ; to each add the remaining seg .; then this produced line and added seg . are less than the sides of original ...
... meet one of the sides , then the whole produced line is less than the uncut side and conterminous segment of cut side ; to each add the remaining seg .; then this produced line and added seg . are less than the sides of original ...
Side 18
... meet on either side , then the ex- ternal angle of the triangle is greater than the internal remote , but it is also = to it , which is absurd : .. the lines will not meet , if produced this way ; and in like manner , it can be proved ...
... meet on either side , then the ex- ternal angle of the triangle is greater than the internal remote , but it is also = to it , which is absurd : .. the lines will not meet , if produced this way ; and in like manner , it can be proved ...
Side 19
... meet , ( by ax 12 , ) since it , with the internal on the same side , would then be less than two right angles ; but since the lines are parallel , they cannot meet , ... the alternate angles are not unequal . And since the alternate ...
... meet , ( by ax 12 , ) since it , with the internal on the same side , would then be less than two right angles ; but since the lines are parallel , they cannot meet , ... the alternate angles are not unequal . And since the alternate ...
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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.