The Elements of Geometry, Symbolically Arranged |
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Σελίδα 10
... deduced from a proposition . An axiom is an evident truth , but which admits of no demonstration . A postulate is a request to admit the possibi- lity of performing an operation . PROP . I. PROB . 1. 1 Eu . To 10 GEOMETRY .
... deduced from a proposition . An axiom is an evident truth , but which admits of no demonstration . A postulate is a request to admit the possibi- lity of performing an operation . PROP . I. PROB . 1. 1 Eu . To 10 GEOMETRY .
Σελίδα 11
... PROB . 2. 1 Eu . From a given point to draw a straight line equal to a given straight line . Let A be the given pt . , and BC the given str . line ; it is required to draw from the pt . A , a str . line BC . Post . 1 . Draw AB ; on AB ...
... PROB . 2. 1 Eu . From a given point to draw a straight line equal to a given straight line . Let A be the given pt . , and BC the given str . line ; it is required to draw from the pt . A , a str . line BC . Post . 1 . Draw AB ; on AB ...
Σελίδα 12
... PROB . 3. 1 Eu . From the greater of two given straight lines , to cut off a part equal to the less . Let AB and C be the given str . lines , where- of AB > C ; it is required to cut off from AB a part = C. Post . 3 . From A draw AD C ...
... PROB . 3. 1 Eu . From the greater of two given straight lines , to cut off a part equal to the less . Let AB and C be the given str . lines , where- of AB > C ; it is required to cut off from AB a part = C. Post . 3 . From A draw AD C ...
Σελίδα 19
... PROB . 9. 1 Eu . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilin . ; it is re- quired to bisect it . Take any point D in AB . From AC cut off AE = AD , Prop . 3 . join ...
... PROB . 9. 1 Eu . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilin . ; it is re- quired to bisect it . Take any point D in AB . From AC cut off AE = AD , Prop . 3 . join ...
Σελίδα 20
... PROB . 10. 1 Eu . To bisect a given finite straight line , that is , to divide it into two equal parts . • To divide AB into two parts . Upon AB descr . equilat . △ ABC . Bisect ACB by CD . Then AB is bisected at D. C Constr . Constr ...
... PROB . 10. 1 Eu . To bisect a given finite straight line , that is , to divide it into two equal parts . • To divide AB into two parts . Upon AB descr . equilat . △ ABC . Bisect ACB by CD . Then AB is bisected at D. C Constr . Constr ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
2ndly ABCD AC² angle contained angle equal base BC CB² centre circle circumference coincides Constr descr diam diameter dist divided equal angles equiangular equilat exterior angle figure given point given str given straight line gnomon greater isosceles triangle join Let ABC Let str Let the str line be drawn meet number of equal oppo opposite angle opposite sides parallel parallelogram perpendicular polygon PROB prod Prop rect rectangle contained rectilineal right angles right-angled triangle semi sides equal square THEOR touch trapezium Wherefore whole fig Нур
Δημοφιλή αποσπάσματα
Σελίδα 60 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 34 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 62 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Σελίδα 38 - Wherefore, if a straight line, &c. QB D. PROPOSITION XXVIII. THEOB.—-If a straight line, falling upon two other straight lines, make the exterior angle equal to...
Σελίδα 63 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 23 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 39 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Σελίδα 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Σελίδα 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 21 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.