Elements of Geometry |
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Page vi
... problems relating to the construction of figures . The third section , entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular ...
... problems relating to the construction of figures . The third section , entitled the proportions of figures , contains the measure of surfaces , their comparison , the properties of a right - angled triangle , those of equiangular ...
Page vii
... problems relating to the objects of which it treats . The fourth section treats of regular polygons and of the meas- ure of the circle . Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the ...
... problems relating to the objects of which it treats . The fourth section treats of regular polygons and of the meas- ure of the circle . Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the ...
Page 3
... problem . The common name of Proposition is given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions ...
... problem . The common name of Proposition is given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions ...
Page 34
... Problems relating to the two first Sections . PROBLEM . 132. To divide a given straight line AB ( fig . 70 ) into two equal parts . Solution . From the points A and B , as centres , and with a radius greater than the half of AB ...
... Problems relating to the two first Sections . PROBLEM . 132. To divide a given straight line AB ( fig . 70 ) into two equal parts . Solution . From the points A and B , as centres , and with a radius greater than the half of AB ...
Page 35
... PROBLEM . 133. From a given point A ( fig . 71 ) , in the line BC , to erect a Fig . 71 . perpendicular to this line . Solution . Take the points B and C , at equal distances from A ; and from B and C , as centres , with a radius ...
... PROBLEM . 133. From a given point A ( fig . 71 ) , in the line BC , to erect a Fig . 71 . perpendicular to this line . Solution . Take the points B and C , at equal distances from A ; and from B and C , as centres , with a radius ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence