# 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 páginas

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### Contenido

 Sección 1 1 Sección 2 3 Sección 3 18 Sección 4 22 Sección 5 33 Sección 6 35 Sección 7 47 Sección 8 75
 Sección 16 194 Sección 17 195 Sección 18 197 Sección 19 204 Sección 20 212 Sección 21 218 Sección 22 221 Sección 23 226

 Sección 9 108 Sección 10 111 Sección 11 114 Sección 12 123 Sección 13 157 Sección 14 161 Sección 15 178
 Sección 24 230 Sección 25 231 Sección 26 234 Sección 27 235 Sección 28 238 Sección 29 243

### Pasajes populares

Página 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.
Página 73 - The radius of a circle is a right line drawn from the centre to the circumference.
Página 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.
Página 207 - 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 241 - 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 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.
Página 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.
Página 157 - 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.