Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and ExplanatoryJohnson, 1803 - 279 páginas |
Dentro del libro
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Página 41
... base of the parallelogram be half that of the triangle , or the base of the triangle be double that of the parallelogram , the two figures will be equal to each other . PROP . 1 PROP . XXXIII . PROBLEM . To make a BOOK THE FIRST , 41.
... base of the parallelogram be half that of the triangle , or the base of the triangle be double that of the parallelogram , the two figures will be equal to each other . PROP . 1 PROP . XXXIII . PROBLEM . To make a BOOK THE FIRST , 41.
Página 43
... half of it , A Let ABC be a triangle , whose fides CA , CB are bisected in the points D , E ; then will the right line DE , joining those points , be parallel to AB , and equal to one half of it . For , in DE produced , take EF equal to ...
... half of it , A Let ABC be a triangle , whose fides CA , CB are bisected in the points D , E ; then will the right line DE , joining those points , be parallel to AB , and equal to one half of it . For , in DE produced , take EF equal to ...
Página 58
... cb . Q. E. D. COROLL . If a line be divided into two equal parts , the fquare of the whole line will be equal to four times the fquare of half the line . PROP . XII . THEOREM . If a right line PROP 58 ELEMENTS OF GEOMETRY .
... cb . Q. E. D. COROLL . If a line be divided into two equal parts , the fquare of the whole line will be equal to four times the fquare of half the line . PROP . XII . THEOREM . If a right line PROP 58 ELEMENTS OF GEOMETRY .
Página 84
... half of AB ( III . 3. ) , and DF is the half of DE ( III . 3. ) , the square of AC is equal to the square of DF ( II . 2. ) The remaining fquare of co is , therefore , equal to the remaining fquare of Fo ; and confequently co is equal ...
... half of AB ( III . 3. ) , and DF is the half of DE ( III . 3. ) , the square of AC is equal to the square of DF ( II . 2. ) The remaining fquare of co is , therefore , equal to the remaining fquare of Fo ; and confequently co is equal ...
Página 92
... half the angle BEC . And , for the fame reason , the angle BDC will , also , be half the angle BEC . But things which are halves of the fame thing are equal to each other ; consequently the angle BAC is equal to the angle BDC . Again ...
... half the angle BEC . And , for the fame reason , the angle BDC will , also , be half the angle BEC . But things which are halves of the fame thing are equal to each other ; consequently the angle BAC is equal to the angle BDC . Again ...
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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 BAD angle CAB bafe baſe becauſe bifect cafe centre chord circle ABC circumference confequently Conft COROLL DABC 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 firſt folid fome fquares of AC given circle given right line infcribe interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reaſon rectangle of AB rectangle of AE remaining angle right angles ſame SCHOLIUM ſhewn ſpace ſquare tangent THEOREM theſe triangle ABC twice the rectangle uſeful whence
Pasajes populares
Página 164 - 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 71 - The radius of a circle is a right line drawn from the centre to the circumference.
Página 69 - 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.
Página 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.
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 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.
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. 5. If equals be taken from unequals, the remainders will be unequal.
Página 133 - 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.
Página 143 - 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.
Página 155 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order.