Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 σελίδες |
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Σελίδα 10
... equal to two fides and the in- cluded angle of another , each to each , the triangles will be equal in all ... same extremities , muft coincide , or otherwise their parts would not lie in ... base PROP . ΙΟ ELEMENTS OF GEOMETRY . A ...
... equal to two fides and the in- cluded angle of another , each to each , the triangles will be equal in all ... same extremities , muft coincide , or otherwise their parts would not lie in ... base PROP . ΙΟ ELEMENTS OF GEOMETRY . A ...
Σελίδα 40
... equal things be taken from the same thing , the remainders will be equal ; confequently , the parallelogram AE is equal to the parallelogram BD .. Again , let ABC , ABF be two triangles , ftanding upon the fame base AB , and between the ...
... equal things be taken from the same thing , the remainders will be equal ; confequently , the parallelogram AE is equal to the parallelogram BD .. Again , let ABC , ABF be two triangles , ftanding upon the fame base AB , and between the ...
Σελίδα 41
... same base AB , and between the fame parallels AB , DE ( Prop . 32. ) ; whence the paral- lelogram AC is also double the triangle AEB . QE . D. COROLL . If the base of the parallelogram be half that of the triangle , or the base of the ...
... same base AB , and between the fame parallels AB , DE ( Prop . 32. ) ; whence the paral- lelogram AC is also double the triangle AEB . QE . D. COROLL . If the base of the parallelogram be half that of the triangle , or the base of the ...
Σελίδα 121
... equal to the two fides ED , EA , and the angle BEA to the angle AED , ( be- ing each of them right angles ) , the base BA will be equal to the base AD ( I. 4. ) And , in the same manner , it may be proved , that the fides BC , CD are each ...
... equal to the two fides ED , EA , and the angle BEA to the angle AED , ( be- ing each of them right angles ) , the base BA will be equal to the base AD ( I. 4. ) And , in the same manner , it may be proved , that the fides BC , CD are each ...
Σελίδα 159
... base HC , and the triangle AHC , are any equi- multiples whatever of the ... equal altitudes , are to each other as their bafes . PRO P. II . Triangles and parallelograms , having equal ... same ratio to the triangle BOOK 159 THE SIXTH .
... base HC , and the triangle AHC , are any equi- multiples whatever of the ... equal altitudes , are to each other as their bafes . PRO P. II . Triangles and parallelograms , having equal ... same ratio to the triangle BOOK 159 THE SIXTH .
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.