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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Σελίδα 7
... centres and the given line as radius , describe two circles , ( per post . 3 ) ; from a point , in which those circles ... centre of either being in the circumference of the other , part of its circum- ference must be within the other ...
... centres and the given line as radius , describe two circles , ( per post . 3 ) ; from a point , in which those circles ... centre of either being in the circumference of the other , part of its circum- ference must be within the other ...
Σελίδα 8
... centre , and the drawn line as an interval , describe a circle ; this circle cuts from the greater line a part to the less . = For the part cut off between the circumference and centre is to the drawn line , which was made to the lesser ...
... centre , and the drawn line as an interval , describe a circle ; this circle cuts from the greater line a part to the less . = For the part cut off between the circumference and centre is to the drawn line , which was made to the lesser ...
Σελίδα 12
... centre , and the interval between the given point and the assumed point as radius , describe a circle , cutting the given line in two points ; bisect the intercept , and connect the given point with the extremities of it , and also with ...
... centre , and the interval between the given point and the assumed point as radius , describe a circle , cutting the given line in two points ; bisect the intercept , and connect the given point with the extremities of it , and also with ...
Σελίδα 16
... centres , and the lines drawn from them as intervals , de- scribe two circles ; and , from one of their intersections , draw lines to the centres ( or the extremities of the first drawn line ) , and the required triangle is formed . For ...
... centres , and the lines drawn from them as intervals , de- scribe two circles ; and , from one of their intersections , draw lines to the centres ( or the extremities of the first drawn line ) , and the required triangle is formed . For ...
Σελίδα 28
Euclides James Luby. becomes to the lesser ; from their common extremity as centre , and the greater as radius , describe a circle , and from the other extremity of produced part , erect a perpendicular to meet its circumference ; the 2 ...
Euclides James Luby. becomes to the lesser ; from their common extremity as centre , and the greater as radius , describe a circle , and from the other extremity of produced part , erect a perpendicular to meet its circumference ; the 2 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 130 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Σελίδα 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.
Σελίδα 32 - ... polygons are to each other in the duplicate ratio of their homologous sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 118 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.