A Supplement to the Elements of EuclidJ. Smith, 1825 - 582 σελίδες |
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Σελίδα 4
... manifest that a circle may be described , which shall have its centre in a given straight line , and which shall pass through two given points without that line . 5. COR . 2. It is evident from the demonstration , that any point in an ...
... manifest that a circle may be described , which shall have its centre in a given straight line , and which shall pass through two given points without that line . 5. COR . 2. It is evident from the demonstration , that any point in an ...
Σελίδα 13
... manifest , that of the segments into which the straight line bisecting the vertical angle of a scalene triangle , divides the base , that which is adjacent to the less side , is the less . PROP . XIV . 22. THEOREM . If a trapezium and a ...
... manifest , that of the segments into which the straight line bisecting the vertical angle of a scalene triangle , divides the base , that which is adjacent to the less side , is the less . PROP . XIV . 22. THEOREM . If a trapezium and a ...
Σελίδα 18
... manifest that it has the same number of sides as the figure ABCDEF . PROP . XVIII . 26. THEOREM . If two opposite sides of a quadri- lateral figure be equal to one another , and the two remaining sides be also equal to one another , the ...
... manifest that it has the same number of sides as the figure ABCDEF . PROP . XVIII . 26. THEOREM . If two opposite sides of a quadri- lateral figure be equal to one another , and the two remaining sides be also equal to one another , the ...
Σελίδα 29
... manifest , therefore , that they will be in the circumference of a circle , described from that point as the centre , at a distance equal to the half of one of the hypotenuses ; and the portion of the cir- cumference , being that which ...
... manifest , therefore , that they will be in the circumference of a circle , described from that point as the centre , at a distance equal to the half of one of the hypotenuses ; and the portion of the cir- cumference , being that which ...
Σελίδα 37
... manifest that the two triangles FAE , EBH have the two sides FA , AE equal to the two EB , BH , each to each , and ( E. xxx . Def . 1. ) the AB ; therefore ( E. IV . 1. ) the AFE = LBEH ; and FE = EH : And , in the same manner , it may ...
... manifest that the two triangles FAE , EBH have the two sides FA , AE equal to the two EB , BH , each to each , and ( E. xxx . Def . 1. ) the AB ; therefore ( E. IV . 1. ) the AFE = LBEH ; and FE = EH : And , in the same manner , it may ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² aggregate angle equal arch bisect centre chord circle ABC circumference constr describe a circle describe the circle diameter distance divided draw E equi equiangular equilateral finite straight line fourth proportional given circle given finite straight given point given ratio given square given straight line greater ratio hypotenuse inscribed isosceles triangle join K less Let AB Let ABC lines be drawn manifest meet the circumference parallel to BC parallelogram polygon PROBLEM produced PROP rectangle contained rectilineal figure remaining sides required to draw rhombus right angles segment semi-diameter shewn straight line joining tangent THEOREM touch the circle trapezium wherefore xlvii xvii xxix xxvi xxviii xxxi xxxii xxxiv
Δημοφιλή αποσπάσματα
Σελίδα 277 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 560 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 564 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 178 - 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...
Σελίδα 557 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one another: and if the segments of the base...
Σελίδα 539 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 325 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the...
Σελίδα 550 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 555 - And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth...
Σελίδα 17 - ... angles equal; and conversely if two angles of a triangle are equal, two of the sides are equal. 3. If two triangles have the three sides of one equal to the three sides of the other, each to each, do you think the two triangles are alike in every respect ? 4. If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5. Draw two triangles, the angles of one being equal to the angles...