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 18
... shall be perpendicular to AB . Take any point D , in AB , and from that point , with the distance DC , defcribe the circle CGE , cutting AB in G. Join GC , and from the point G , with the distance GC , describe the circle n E m ...
... shall be perpendicular to AB . Take any point D , in AB , and from that point , with the distance DC , defcribe the circle CGE , cutting AB in G. Join GC , and from the point G , with the distance GC , describe the circle n E m ...
Σελίδα 25
... shall be equal to three given right lines , provided any two of them , taken together , be greater than the third . E A B C Let A , B , c be the three given right lines , any two of which , taken together , are greater than the third ...
... shall be equal to three given right lines , provided any two of them , taken together , be greater than the third . E A B C Let A , B , c be the three given right lines , any two of which , taken together , are greater than the third ...
Σελίδα 35
... shall be parallel to AB . Take any point D in AB , and make DE equal to DC ( Prop . 3. ) ; and from the points c , E , with the distances CD , ED , defcribe the arcs rs , nm . Then , fince any two fides of the triangle ECD are , to ...
... shall be parallel to AB . Take any point D in AB , and make DE equal to DC ( Prop . 3. ) ; and from the points c , E , with the distances CD , ED , defcribe the arcs rs , nm . Then , fince any two fides of the triangle ECD are , to ...
Σελίδα 42
... shall have its oppofite fides equal to two given right lines , and one of its angles equal to a given rectilineal angle . F B с Let AB and c be two given right lines , and D a given rectilineal angle ; it is required to make a ...
... shall have its oppofite fides equal to two given right lines , and one of its angles equal to a given rectilineal angle . F B с Let AB and c be two given right lines , and D a given rectilineal angle ; it is required to make a ...
Σελίδα 71
... shall be equal to the fquare of the other part . B Ꮐ Н E Let AB be the given right line ; it is required to divide it into two parts , fo that the rectangle of the whole line and one of the parts fhall be equal to the fquare of the ...
... shall be equal to the fquare of the other part . B Ꮐ Н E Let AB be the given right line ; it is required to divide it into two parts , fo that the rectangle of the whole line and one of the parts fhall be equal to the fquare of the ...
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.