The Elements of Euclid, books i. to vi., with deductions, appendices and historical notes, by J.S. Mackay. [With] Key1884 |
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Resultat 1-5 av 13
Side 103
... fixed point . Suppose D to be any point on the locus , and join DA , DB , DC . Then DA = : DB ; Нур . and since DC is common , and AC = BC , .. DC is 1 AB . B Const . I. 8 , Def . 10 Hence , if a set of other points on the locus be ...
... fixed point . Suppose D to be any point on the locus , and join DA , DB , DC . Then DA = : DB ; Нур . and since DC is common , and AC = BC , .. DC is 1 AB . B Const . I. 8 , Def . 10 Hence , if a set of other points on the locus be ...
Side 104
... fixed point , C the centre of the given fixed circle ; let AB , one of the straight lines drawn from A to the Oce , be bisected at E : it is required to find the locus of E. Join AC , and bisect it at D ; I. 10 join DE and CB . Because ...
... fixed point , C the centre of the given fixed circle ; let AB , one of the straight lines drawn from A to the Oce , be bisected at E : it is required to find the locus of E. Join AC , and bisect it at D ; I. 10 join DE and CB . Because ...
Side 150
... fixed length ; that is , the vertex of any triangle fulfilling the given conditions is always at a constant distance from a fixed point D , the middle of the given base . Hence , the locus required is the Oce of a circle whose centre is ...
... fixed length ; that is , the vertex of any triangle fulfilling the given conditions is always at a constant distance from a fixed point D , the middle of the given base . Hence , the locus required is the Oce of a circle whose centre is ...
Side 151
... fixed circle is the middle point of the base of a triangle . If the vertex of the triangle be on the " , the sum of the squares on the two sides of the triangle is con- stant . 6. The centre of a fixed circle is the point of ...
... fixed circle is the middle point of the base of a triangle . If the vertex of the triangle be on the " , the sum of the squares on the two sides of the triangle is con- stant . 6. The centre of a fixed circle is the point of ...
Side 152
... fixed points , and O any other point , the sum of the squares on OA and OB is least when O is the middle point of AB . 13. Prove II . 9 , 10 by the following construction : On AD describe a rectangle A EFD whose sides AE , DF are each ...
... fixed points , and O any other point , the sum of the squares on OA and OB is least when O is the middle point of AB . 13. Prove II . 9 , 10 by the following construction : On AD describe a rectangle A EFD whose sides AE , DF are each ...
Andre utgaver - Vis alle
The Elements of Euclid, books i. to vi., with deductions, appendices and ... Euclides Uten tilgangsbegrensning - 1885 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon Mackay,John Sturgeon Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon MacKay,John Sturgeon Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
AB² ABCD AC² AD² angles equal base BC bisected bisector CD² centre chord circumscribed Const deduction diagonals diameter divided in medial divided internally draw equiangular equilateral triangle equimultiples Euclid's exterior angles Find the locus given circle given point given straight line greater Hence hypotenuse inscribed intersection isosceles triangle less Let ABC lines is equal magnitudes medial section median meet middle points opposite sides orthocentre parallel parallelogram perpendicular polygon produced PROPOSITION 13 Prove the proposition quadrilateral radical axis radii radius ratio rectangle contained rectilineal figure regular pentagon required to prove rhombus right angle right-angled triangle square on half straight line drawn straight line joining tangent THEOREM unequal segments vertex vertical angle Нур
Populære avsnitt
Side 147 - 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.
Side 276 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words
Side 331 - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Side 17 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Side 112 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 87 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 254 - If there be four magnitudes, and if any equimultiples whatsoever be taken of the first and third, and any equimultiples whatsoever of the second and fourth, and if, according as the multiple of the first is greater than the multiple of the second, equal to it or less, the multiple of the third is also greater than the multiple of the fourth, equal to it or less ; then, the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth.
Side 138 - RULE. from half the sum of the three sides, subtract each side separately; multiply the half sum and the three remainders together, and the square root of the product will be the area required.
Side 304 - 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 44 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.