The Elements of Euclid, books i. to vi., with deductions, appendices and historical notes, by J.S. Mackay. [With] Key1884 |
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... PROPORTIONAL SECTION AND SIMILAR FIGURES— DEFINITIONS ... ..286 PROPOSITIONS 1-33 WITH RIDERS . .287 PROPOSITION A .. .294 PROPOSITIONS B , C , D .. 338 APPENDIX VI . TRANSVERSALS ... .343 HARMONICAL PROGRESSION .. .347 DEDUCTIONS ...
... PROPORTIONAL SECTION AND SIMILAR FIGURES— DEFINITIONS ... ..286 PROPOSITIONS 1-33 WITH RIDERS . .287 PROPOSITION A .. .294 PROPOSITIONS B , C , D .. 338 APPENDIX VI . TRANSVERSALS ... .343 HARMONICAL PROGRESSION .. .347 DEDUCTIONS ...
Página 262
... proportional , they consti- tute a proportion . The first and last terms of the proportion are called the extremes ; the second and third , the means . 9. When of the equimultiples of four magnitudes , taken as in the fifth definition ...
... proportional , they consti- tute a proportion . The first and last terms of the proportion are called the extremes ; the second and third , the means . 9. When of the equimultiples of four magnitudes , taken as in the fifth definition ...
Página 263
... proportional between the other two . Three magnitudes in continued proportion are sometimes said to be in geometrical progression , and the mean proportional is then called a geometric mean between the other two . 12. When there is any ...
... proportional between the other two . Three magnitudes in continued proportion are sometimes said to be in geometrical progression , and the mean proportional is then called a geometric mean between the other two . 12. When there is any ...
Página 269
... proportional by inversion . Let A B : = C : D : it is required to prove B : A = D : C. Let mA and mC be any equimultiples of A and C , nB and nD any equimultiples of B and D. Then , because A : B = C : D , if mA be less than nB , mC ...
... proportional by inversion . Let A B : = C : D : it is required to prove B : A = D : C. Let mA and mC be any equimultiples of A and C , nB and nD any equimultiples of B and D. Then , because A : B = C : D , if mA be less than nB , mC ...
Página 277
... proportional by alternation . Let A : B = C : D : it is required to prove A : C = B : D. Take mA , mB any equimultiples of A and B , and nC , nD any equimultiples of C and D. Then A : B V. 15 = MA : mB . But A : B = C : D ; C : D = MA ...
... proportional by alternation . Let A : B = C : D : it is required to prove A : C = B : D. Take mA , mB any equimultiples of A and B , and nC , nD any equimultiples of C and D. Then A : B V. 15 = MA : mB . But A : B = C : D ; C : D = MA ...
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.