The Elements of Euclid, books i. to vi., with deductions, appendices and historical notes, by J.S. Mackay. [With] Key1884 |
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Página 12
... doubles of the same thing are equal to one another . 7. Things which are halves of the same thing are equal to one another . 8. The whole is greater than its part , and equal to the sum of all its parts . 9. Magnitudes which coincide ...
... doubles of the same thing are equal to one another . 7. Things which are halves of the same thing are equal to one another . 8. The whole is greater than its part , and equal to the sum of all its parts . 9. Magnitudes which coincide ...
Página 13
... double of equals are equal , and Things which are halves of equals are equal ; and these axioms again are only particular cases of still more general ones : Similar multiples of equals ( or of the same thing ) are equal , and Similar ...
... double of equals are equal , and Things which are halves of equals are equal ; and these axioms again are only particular cases of still more general ones : Similar multiples of equals ( or of the same thing ) are equal , and Similar ...
Página 23
... double of AB . 5. AB is a given straight line ; show how to draw through B any number of straight lines double of AB . 6. On a given straight line as base , describe an isosceles triangle each of whose sides shall be equal to a given ...
... double of AB . 5. AB is a given straight line ; show how to draw through B any number of straight lines double of AB . 6. On a given straight line as base , describe an isosceles triangle each of whose sides shall be equal to a given ...
Página 25
... double of the greater straight line . 7. Show that if the difference of two straight lines be taken away from the sum of the two straight lines , the result will be double of the less straight line . PROPOSITION 4 . THEOREM . If two ...
... double of the greater straight line . 7. Show that if the difference of two straight lines be taken away from the sum of the two straight lines , the result will be double of the less straight line . PROPOSITION 4 . THEOREM . If two ...
Página 34
... double of the other , the hypot- enuse is double of the side opposite the least angle . PROPOSITION 10 . PROBLEM . To bisect a given straight 34 [ Book L EUCLID'S ELEMENTS .
... double of the other , the hypot- enuse is double of the side opposite the least angle . PROPOSITION 10 . PROBLEM . To bisect a given straight 34 [ Book L EUCLID'S ELEMENTS .
Otras ediciones - Ver todas
The Elements of Euclid, books i. to vi., with deductions, appendices and ... Euclides Vista completa - 1885 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon Mackay,John Sturgeon Euclides Sin vista previa disponible - 2018 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon MacKay,John Sturgeon Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.