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].1814 |
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Αποτελέσματα 1 - 5 από τα 77.
Σελίδα
... solid angles of the figures is contained by no more than three plane angles ; for in other cases , two solid figures may be contained by similar planes of the same number and magnitude , and yet be unequal to one another , as shall be ...
... solid angles of the figures is contained by no more than three plane angles ; for in other cases , two solid figures may be contained by similar planes of the same number and magnitude , and yet be unequal to one another , as shall be ...
Σελίδα 188
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles , to a plane , when it makes right angles with every straight line ...
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles , to a plane , when it makes right angles with every straight line ...
Σελίδα 189
... solid figures are such as have all their solid angles See N equal , each to each , and which are contained by the same number of similar planes . XII . A pyramid is a solid figure contained by planes that are constituted betwixt one ...
... solid figures are such as have all their solid angles See N equal , each to each , and which are contained by the same number of similar planes . XII . A pyramid is a solid figure contained by planes that are constituted betwixt one ...
Σελίδα 190
... solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed ... solid figure contained by six equal squares . XXVI . A tetrahedron is a solid figure contained by four equal and ...
... solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed ... solid figure contained by six equal squares . XXVI . A tetrahedron is a solid figure contained by four equal and ...
Σελίδα 205
... solid angle at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the ... solid angle , & c . Q. E. D. PROP . XXI . THEOR . EVERY solid angle is contained by plane angles , which together are ...
... solid angle at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the ... solid angle , & c . Q. E. D. PROP . XXI . THEOR . EVERY solid angle is contained by plane angles , which together are ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 3-7 - 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.
Σελίδα 16 - Any two sides of a triangle are together greater than the third side.
Σελίδα 26 - 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.
Σελίδα 16 - 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...
Σελίδα 304 - 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.
Σελίδα 4 - 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.
Σελίδα 147 - 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.
Σελίδα 3-16 - 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.
Σελίδα 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.