A System of Popular Geometry: Containing in a Few Lessons So Much of the Elements of Euclid as is Necessary and Sufficient for a Right Understanding of Every Art and Science in Its Leading Truths and General PrinciplesTaylor and Walton, Booksellers to the University of London, 30 Upper Gower Street, 1836 - 128 σελίδες |
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Σελίδα xii
... theorems under one head , as is frequently done in Euclid , we have separated and proved them distinctly . Where the proofs in Euclid appeared difficult , unsatisfactory , or prolix * , we have substituted easier , clearer , and shorter ...
... theorems under one head , as is frequently done in Euclid , we have separated and proved them distinctly . Where the proofs in Euclid appeared difficult , unsatisfactory , or prolix * , we have substituted easier , clearer , and shorter ...
Σελίδα xiii
... Theorems and Problems . A Theorem asserts that such a result will take place on such a condition ; as , that— " if a triangle have two equal legs , it will also have two equal angles . " A problem requires something to be done ; such as ...
... Theorems and Problems . A Theorem asserts that such a result will take place on such a condition ; as , that— " if a triangle have two equal legs , it will also have two equal angles . " A problem requires something to be done ; such as ...
Σελίδα xiv
... theorems ; and they are so arranged that every problem assumed in a theorem precedes that theorem , while every theorem on which a problem depends precedes that problem . So that both theorems and problems may be read together as in ...
... theorems ; and they are so arranged that every problem assumed in a theorem precedes that theorem , while every theorem on which a problem depends precedes that problem . So that both theorems and problems may be read together as in ...
Σελίδα xix
... theorems and problems are contained , so that no reference to any other treatise may be necessary . In this manner have we compiled a brief System of Geo- metry for popular use . It contains all of the Science which is necessary for the ...
... theorems and problems are contained , so that no reference to any other treatise may be necessary . In this manner have we compiled a brief System of Geo- metry for popular use . It contains all of the Science which is necessary for the ...
Σελίδα xx
... Theorems and Problems , which were excluded from the text for their irrelevancy , but which are collected here for their utility . Thus are all the useful principles and propositions of Euclid collected in a small , unexpensive volume ...
... Theorems and Problems , which were excluded from the text for their irrelevancy , but which are collected here for their utility . Thus are all the useful principles and propositions of Euclid collected in a small , unexpensive volume ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitudes angle ABC angle BAC angle CDA angles EAB angles equal base AC centre chord circumference Consequently contained definition demonstration equal arches equal bases equal circles equal sides equal to CD equal to four equal triangles equally distant equi-angular Euclid finite right line Geometry given finite right given point given right line greater Hence ibid internal angles Join KLMN Let ABC line CD lines be drawn magnitude NOTE opposite angles parallel right lines parallelogram perpendicular PROB produced propositions quantities reciprocally proportional rectangle rectilineal figure respectively equal right angles right line divided right line drawn right line intersect segments side AB side AC square of AB square of AC submultiple supposition is false tangent theorem third side three sides tiples triangle ABC unequal vertex
Δημοφιλή αποσπάσματα
Σελίδα 31 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Σελίδα xxxi - 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 3 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα xxx - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 30 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Σελίδα 25 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.
Σελίδα 99 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Σελίδα 51 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...
Σελίδα 10 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 11 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.