Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryMarot & Walter, 1826 - 320 páginas |
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Página viii
... be indefinitely varied , is capable of all degrees of magnitude , from nothing upwards , ) and yet it may in many cases be a problem of extreme difficulty to assign the height of 2 such a solid , and actually to exhibit it viii PREFACE .
... be indefinitely varied , is capable of all degrees of magnitude , from nothing upwards , ) and yet it may in many cases be a problem of extreme difficulty to assign the height of 2 such a solid , and actually to exhibit it viii PREFACE .
Página 13
... magnitude . " * A ( See Notes . ) II . A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the in- * tersections of one line with another are also points . ” III . " If two lines are such that ...
... magnitude . " * A ( See Notes . ) II . A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the in- * tersections of one line with another are also points . ” III . " If two lines are such that ...
Página 17
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. All right angles are equal to one another . XI . Two straight lines which ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. All right angles are equal to one another . XI . Two straight lines which ...
Página 49
... magnitudes , signi- " fies that those magnitudes are to be added together , and the sign " — placed between them , signifies that the latter is to be taken away from the former . " " The sign = signifies , that the things between which ...
... magnitudes , signi- " fies that those magnitudes are to be added together , and the sign " — placed between them , signifies that the latter is to be taken away from the former . " " The sign = signifies , that the things between which ...
Página 102
... magnitudes of any kind . The letters m , n , p , q , are used to denote numbers only . " 2. The sign + ( plus ) , written between two letters , that denote magnitudes or numbers , signifies the sum of those magnitudes or numbers . Thus ...
... magnitudes of any kind . The letters m , n , p , q , are used to denote numbers only . " 2. The sign + ( plus ) , written between two letters , that denote magnitudes or numbers , signifies the sum of those magnitudes or numbers . Thus ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 125 - 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 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Página 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Página 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Página 30 - 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.
Página 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Página 51 - 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 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Página 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.