Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 páginas |
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Página 47
... square , Let AB be the given right line ; it is required to de- fcribe a fquare upon it . Make AD , BC , each perpendicular and equal to AB ( I. 11 and 3. ) , and join DC ; then will AC be the fquare required For , fince the angles DAB ...
... square , Let AB be the given right line ; it is required to de- fcribe a fquare upon it . Make AD , BC , each perpendicular and equal to AB ( I. 11 and 3. ) , and join DC ; then will AC be the fquare required For , fince the angles DAB ...
Página 48
... AC , therefore , being both equilateral and rectangular , is a square ; and it is defcribed upon the line AB , as was to be done . PROP . II . THEOREM . Rectangles and Squares contained under equal lines are equal to each other . D A H ...
... AC , therefore , being both equilateral and rectangular , is a square ; and it is defcribed upon the line AB , as was to be done . PROP . II . THEOREM . Rectangles and Squares contained under equal lines are equal to each other . D A H ...
Página 53
... AC is a parallelogram , whofe diagonal is BD , the triangle DAB will be equal to the triangle BCD ( I. 30. ) And ... square , and HE , FG parallelograms about its diagonal AC ; then will those parallelograms also be fquares . For fince ...
... AC is a parallelogram , whofe diagonal is BD , the triangle DAB will be equal to the triangle BCD ( I. 30. ) And ... square , and HE , FG parallelograms about its diagonal AC ; then will those parallelograms also be fquares . For fince ...
Página 56
... AC , it is also contained by AB , AC , because AE is equal to AB ( II . Def . 2. ) And , fince the rectangle CD is ... square of AB . Q. E. D. PROP . X. THEOREM . If a right line be divided into any two parts , the rectangle of the whole line ...
... AC , it is also contained by AB , AC , because AE is equal to AB ( II . Def . 2. ) And , fince the rectangle CD is ... square of AB . Q. E. D. PROP . X. THEOREM . If a right line be divided into any two parts , the rectangle of the whole line ...
Página 57
... square of AB be equal to the fquares of AC , CB together with twice the rectangle of AC , CB . For upon AB make the fquare AD ( II . 1. ) , and draw the diagonal EB ; and make CK , FH parallel to AE , ed ( I , 27. ) : Then , Then ...
... square of AB be equal to the fquares of AC , CB together with twice the rectangle of AC , CB . For upon AB make the fquare AD ( II . 1. ) , and draw the diagonal EB ; and make CK , FH parallel to AE , ed ( I , 27. ) : Then , Then ...
Otras ediciones - Ver todas
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD AC is equal alfo equal alſo be equal alſo be greater altitude angle ABC angle ACB angle BAC angle CAB angle DAF bafe baſe becauſe bifect cafe centre chord circle ABC circumference Conft defcribe demonftration diagonal diameter diſtance draw EFGH equiangular equimultiples EUCLID fame manner fame multiple fame plane fame ratio fecond fection fegment fhewn fide AB fide AC fimilar fince the angles folid fome fquares of AC ftand given circle given right line infcribed interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelepipedons parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reafon rectangle of AB rectangle of AC remaining angle right angles SCHOLIUM ſhall ſpace ſquare tangent THEOREM theſe thofe thoſe triangle ABC twice the rectangle whence
Pasajes populares
Página 166 - 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 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 215 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Página 117 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw the straight line GAH touching the circle in the point A (III. 17), and at the point A, in the straight line AH, make the angle HAG equal to the angle DEF (I.
Página 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Página 249 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 102 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Página i - Handbook to the First London BA Examination. Lie (Jonas). SECOND SIGHT; OR, SKETCHES FROM NORDLAND. By JONAS LIE. Translated from the Norwegian. [/» preparation. Euclid. THE ENUNCIATIONS AND COROLLARIES of the Propositions in the First Six and the Eleventh and Twelfth Books of Euclid's Elements.
Página 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.
Página 145 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.