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
Resultados 6-10 de 32
Página 160
... altitudes , are the double of these triangles , they will , like- wife , have to each other the same ratio as their altitudes . Q. E. D. COR . 1. If the bases of equal triangles are equal , the altitudes will also be equal ; and if the ...
... altitudes , are the double of these triangles , they will , like- wife , have to each other the same ratio as their altitudes . Q. E. D. COR . 1. If the bases of equal triangles are equal , the altitudes will also be equal ; and if the ...
Página 161
... altitude are to each other as their bafes ( VI . 1. ) ; whence the triangle DBE will be to the triangle DAE as DB is to`DA . For the fame reason , the triangle DCE will be to the triangle DAE , as EC is to EA . M And , And , fince ...
... altitude are to each other as their bafes ( VI . 1. ) ; whence the triangle DBE will be to the triangle DAE as DB is to`DA . For the fame reason , the triangle DCE will be to the triangle DAE , as EC is to EA . M And , And , fince ...
Página 162
... altitudes ( VI . 2. Cor . ) , or ftand between the fame parallels ; whence DE is parallel to BC . Q.E.D. COROLL . In the fame manner it may be fhewn , that the fides of the triangle are proportional to any two of the parts into which ...
... altitudes ( VI . 2. Cor . ) , or ftand between the fame parallels ; whence DE is parallel to BC . Q.E.D. COROLL . In the fame manner it may be fhewn , that the fides of the triangle are proportional to any two of the parts into which ...
Página 173
... altitudes , are to each other as their bafes ( VI . 1. ) the parallelogram AH will be to the parallelogram CK , as AB is to CD . And fince AB is to CD as E is to F ( by Hyp . ) , or as DG is to DK ( by Conft . ) , the parallelogram AH ...
... altitudes , are to each other as their bafes ( VI . 1. ) the parallelogram AH will be to the parallelogram CK , as AB is to CD . And fince AB is to CD as E is to F ( by Hyp . ) , or as DG is to DK ( by Conft . ) , the parallelogram AH ...
Página 174
... altitudes are to each other as their bases ( VI . 2. ) , the rectangle AH will be to the rectangle CK as AB is to CD . And , because the rectangle AH is equal to the rectangle CG ( by Hyp . ) , CG will also be to CK as AB is to CD ( V ...
... altitudes are to each other as their bases ( VI . 2. ) , the rectangle AH will be to the rectangle CK as AB is to CD . And , because the rectangle AH is equal to the rectangle CG ( by Hyp . ) , CG will also be to CK as AB is to CD ( V ...
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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.