A Supplement to the Elements of EuclidJ. Smith, 1825 - 582 sider |
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Side 15
... the three angles of the one equal to the three angles of the other , each to each , and if a side of the one be equal to the perpendicular let fall from the right angle upon the hypotenuse of the other , then shall BOOK I. 15.
... the three angles of the one equal to the three angles of the other , each to each , and if a side of the one be equal to the perpendicular let fall from the right angle upon the hypotenuse of the other , then shall BOOK I. 15.
Side 16
... hypotenuse EF of the ADEF : The side DE , of the ADEF , is equal to the hypotenuse AB , of the ABC . For , since AC = DG , and the two 48 ACB , ABC , of the ABC , are equal to the two angles , DGE , DEG , of the ADEG , each to each ...
... hypotenuse EF of the ADEF : The side DE , of the ADEF , is equal to the hypotenuse AB , of the ABC . For , since AC = DG , and the two 48 ACB , ABC , of the ABC , are equal to the two angles , DGE , DEG , of the ADEG , each to each ...
Side 22
... hypotenuse of a right- angled triangle , to find a point , the perpendicular distance of which from one of the sides , shall be equal to the segment of the hypotenuse between the point and the other side . Let ABC be a right - angled ...
... hypotenuse of a right- angled triangle , to find a point , the perpendicular distance of which from one of the sides , shall be equal to the segment of the hypotenuse between the point and the other side . Let ABC be a right - angled ...
Side 29
... hypotenuse for its radius . For , the bisections of the hypotenuses will , each of them , ( Supp . xxix . 1. ) be at ... hypotenuse of a right - angled triangle as a centre , at the distance of half the hypotenuse , BOOK I. 29.
... hypotenuse for its radius . For , the bisections of the hypotenuses will , each of them , ( Supp . xxix . 1. ) be at ... hypotenuse of a right - angled triangle as a centre , at the distance of half the hypotenuse , BOOK I. 29.
Side 30
Daniel Cresswell. centre , at the distance of half the hypotenuse , will pass through the summit of the right angle . 42. COR . 3. The vertical angle of a triangle being a right angle , a point in the base , which is equidistant from the ...
Daniel Cresswell. centre , at the distance of half the hypotenuse , will pass through the summit of the right angle . 42. COR . 3. The vertical angle of a triangle being a right angle , a point in the base , which is equidistant from the ...
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Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 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'.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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...
Side 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.
Side 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...
Side 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...