The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |
Dentro del libro
Página 40
Let AB be the given straight line ; It is required to describe a square upon AB . ... Let ABC be a rigbt - angled triangle having the right angle BAC ; the square described upon the side BC is equal to the squares described upon BA ...
Let AB be the given straight line ; It is required to describe a square upon AB . ... Let ABC be a rigbt - angled triangle having the right angle BAC ; the square described upon the side BC is equal to the squares described upon BA ...
Página 181
Upon AB describe a the square BC , and to AC apply the Book'VI ! parallelogram CD , equal to BC , exceeding by the ... Let ABC be a right angled triangle , having the right angle BAC : The rectilineal figure described upon BC is equal ...
Upon AB describe a the square BC , and to AC apply the Book'VI ! parallelogram CD , equal to BC , exceeding by the ... Let ABC be a right angled triangle , having the right angle BAC : The rectilineal figure described upon BC is equal ...
Página 424
Let the triangle ABC have the given angle BAC , and let the ratio of the rectangle BA , AC , to the square of BC be given ... right angles ; the ratio of AD to BC , that is , of HF to FL , must not be greater than the ratio of MN to BC ...
Let the triangle ABC have the given angle BAC , and let the ratio of the rectangle BA , AC , to the square of BC be given ... right angles ; the ratio of AD to BC , that is , of HF to FL , must not be greater than the ratio of MN to BC ...
Página 430
Draw LR parallel to GP , and from P draw PR at right angles to GP . ... must necessarily cut LR in two points ; let these be 0 , S , and join OG , OH ; SG , SH : each of the triangles OGH , SGH , have the things mentioned to be given in ...
Draw LR parallel to GP , and from P draw PR at right angles to GP . ... must necessarily cut LR in two points ; let these be 0 , S , and join OG , OH ; SG , SH : each of the triangles OGH , SGH , have the things mentioned to be given in ...
Página 478
In any plane triangle BAC , whose two sides are BA , AC , and base BC , the less of the two sides , which let be BA ... And since EBF , FGD are right angles , EB is parallel to GD , and the triangles EBF , FGD are similar ; therefore EB ...
In any plane triangle BAC , whose two sides are BA , AC , and base BC , the less of the two sides , which let be BA ... And since EBF , FGD are right angles , EB is parallel to GD , and the triangles EBF , FGD are similar ; therefore EB ...
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Términos y frases comunes
added altitude angle ABC angle BAC arch base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC Take taken THEOR third triangle ABC wherefore whole
Pasajes populares
Página 45 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 20 - Any two sides of a triangle are together greater than the third side.
Página 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Página 312 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.
Página 155 - 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 54 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Página 167 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Información bibliográfica
| Título | The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |
| Autor | Euclides |
| Editor | Robert Simson |
| Edición | 16 |
| Publicado | 1814 |
| Procedencia del original | Universidad de Oxford |
| Digitalizado | 19 Abr. 2006 |
| Exportar cita | BiBTeX EndNote RefMan |