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. 31821 |
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Σελίδα 4
... third sides shall be equal , also the angles at the bases . shall be equal , viz . those opposite the equal sides , and the whole triangles shall be equal . If the two triangles be so applied to one another , that the vertex of one may ...
... third sides shall be equal , also the angles at the bases . shall be equal , viz . those opposite the equal sides , and the whole triangles shall be equal . If the two triangles be so applied to one another , that the vertex of one may ...
Σελίδα 7
... third sides = ( viz . sides of equilat . trian . ) .. the angles con- tained by the common side and assumed portions are = ( per prop 8 , ) which are the parts of given angle . .. & c . Cor . By this prop . an angle can be divided in 4 ...
... third sides = ( viz . sides of equilat . trian . ) .. the angles con- tained by the common side and assumed portions are = ( per prop 8 , ) which are the parts of given angle . .. & c . Cor . By this prop . an angle can be divided in 4 ...
Σελίδα 11
... third . Bisect the angle contained by the two sides , the bisecting line shall cut the third side into segments which are severally less than their conterminous sides since they are opposite to lesser angles , ( for the angle sub ...
... third . Bisect the angle contained by the two sides , the bisecting line shall cut the third side into segments which are severally less than their conterminous sides since they are opposite to lesser angles , ( for the angle sub ...
Σελίδα 12
... third to construct a triangle , whose sides shall be respectively equal to the three given lines . From any point draw a right line to one of them and from the extremities of this , draw right lines rés- pectively to the other two , and ...
... third to construct a triangle , whose sides shall be respectively equal to the three given lines . From any point draw a right line to one of them and from the extremities of this , draw right lines rés- pectively to the other two , and ...
Σελίδα 13
... third side of the one be greater than the third side of the other , the angle opposite the greater side is greater than the angle which is opposite the lesser . For if it be not greater , it is either to it , or less than it ; it is not ...
... third side of the one be greater than the third side of the other , the angle opposite the greater side is greater than the angle which is opposite the lesser . For if it be not greater , it is either to it , or less than it ; it is not ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent ANALYSIS angle ABC angle contained arches bisecting line chord circumference connecting line conterminous dedu describe a circle diagonal diameter directum divided draw a right drawn line equiangular equilateral triangle evident external angle extremity given angle given circle given in position given line given point given ratio given right line given side gonal half the given hypothenuse inscribed intercept intersect isosceles triangle less lesser let fall line bisecting lines be drawn magnitude mean proportional meet middle point opposite angle opposite side parallelogram pass pendicular perpen perpendicular point of bisection point of contact point of section polygons PORISMS PROB PROP radii radius rect rectangle required triangle right angled triangle right line drawn segts semicircle semiperimeter side subtending square Suppose tangent THEOR triangle ABC vertex vertical angle whole line
Δημοφιλή αποσπάσματα
Σελίδα 128 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Σελίδα 26 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Σελίδα 111 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...
Σελίδα 4 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Σελίδα 98 - 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 2 - 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 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 116 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Σελίδα 156 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Σελίδα 28 - Similar triangles are to one another in the duplicate ratio of their homologous sides.