Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and Explanatory
Johnson, 1803 - 279 pages
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ABCD alfo alfo equal alſo be equal altitude angle ABC bafe baſe becauſe bifect Book centre chord circle circle ABC circumference common confequently Conft contained defcribe definition demonftration diagonal diameter difference divided double draw drawn equiangular equimultiples EUCLID fall fame manner fame multiple fame ratio fection fegment fhewn fide fide AC figure fince folid fome four fquare fquares of AC given given right line greater half interfect join the points lefs leſs Let ABC magnitudes mean meet muſt oppofite parallel parallelogram perpendicular plane polygon PROBLEM produced PROP propofition proportional proved pyramid reaſon rectangle rectangle of AC remaining angle right angles right line ſquare taken tangent THEOREM theſe thing third thoſe triangle triangle ABC twice VIII whence whole
Page 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.
Page 71 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 205 - 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.
Page 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.
Page 239 - 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.
Page 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. 5. If equals be taken from unequals, the remainders will be unequal.
Page 135 - If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest.
Page 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.