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 86
Side
... PROPOSITIONS 1-48 WITH RIDERS . PROPOSITION A .. APPENDIX I. PROPOSITIONS 1-5 ... 98 LOCI . .102 DEDUCTIONS .. .105 18 19 21 61 BOOK II . RECTANGLES AND SQUARES— DEFINITIONS ......... .112 PROPOSITIONS 1-14 WITH RIDERS .. ... 116 ...
... PROPOSITIONS 1-48 WITH RIDERS . PROPOSITION A .. APPENDIX I. PROPOSITIONS 1-5 ... 98 LOCI . .102 DEDUCTIONS .. .105 18 19 21 61 BOOK II . RECTANGLES AND SQUARES— DEFINITIONS ......... .112 PROPOSITIONS 1-14 WITH RIDERS .. ... 116 ...
Side
... PROPOSITIONS 1-16 WITH RIDERS . .224 APPENDIX IV . PROPOSITIONS 1-2 .. .250 DEDUCTIONS ........ .... 256 BOOK V. PROPORTION IN GENERAL— DEFINITIONS ........ AXIOMS ... PROPOSITIONS 1-24 .. PROPOSITIONS A , B , C .... PROPOSITION D ...
... PROPOSITIONS 1-16 WITH RIDERS . .224 APPENDIX IV . PROPOSITIONS 1-2 .. .250 DEDUCTIONS ........ .... 256 BOOK V. PROPORTION IN GENERAL— DEFINITIONS ........ AXIOMS ... PROPOSITIONS 1-24 .. PROPOSITIONS A , B , C .... PROPOSITION D ...
Side 18
... propositions , recourse is sometimes had to the following method . The proposition is supposed not to be true , and the con- sequences of this supposition are then examined , till at 18 [ Book I. EUCLID'S ELEMENTS . EXPLANATION OF TERMS.
... propositions , recourse is sometimes had to the following method . The proposition is supposed not to be true , and the con- sequences of this supposition are then examined , till at 18 [ Book I. EUCLID'S ELEMENTS . EXPLANATION OF TERMS.
Side 20
... proposition . Thus , I. 47 means the forty - seventh proposition of the first book . In the figures to certain of the theorems , it will be seen that some lines are thick , and some dotted . The thick lines are those which are given ...
... proposition . Thus , I. 47 means the forty - seventh proposition of the first book . In the figures to certain of the theorems , it will be seen that some lines are thick , and some dotted . The thick lines are those which are given ...
Side 21
Euclides John Sturgeon Mackay. PROPOSITION 1 . PROBLEM . To describe an equilateral triangle on a given straight line . D Let AB be the given straight line : it is required to describe an ... PROPOSITION 1 . 21 PROPOSITIONS 1-48 WITH RIDERS.
Euclides John Sturgeon Mackay. PROPOSITION 1 . PROBLEM . To describe an equilateral triangle on a given straight line . D Let AB be the given straight line : it is required to describe an ... PROPOSITION 1 . 21 PROPOSITIONS 1-48 WITH RIDERS.
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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.