Euclidian Geometry |
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Page viii
... greater length should occupy pages facing each other : so also that propositions and the corresponding converse ones should be placed on opposite pages . Moreover , Definitions and Axioms , instead of being all at the beginning of the ...
... greater length should occupy pages facing each other : so also that propositions and the corresponding converse ones should be placed on opposite pages . Moreover , Definitions and Axioms , instead of being all at the beginning of the ...
Page xv
... greater than . < less than . ... because . ... therefore . : is to . The object aimed at is merely to place before the student the various steps of an argument in a more succinct form by curtailing the verbiage , thus enabling him to ...
... greater than . < less than . ... because . ... therefore . : is to . The object aimed at is merely to place before the student the various steps of an argument in a more succinct form by curtailing the verbiage , thus enabling him to ...
Page xvi
... greater than another . any multiple of the former is greater than the same multiple of the latter . If a multiple of one magnitude be greater than the same multiple of another then the former magnitude is greater than the latter ...
... greater than another . any multiple of the former is greater than the same multiple of the latter . If a multiple of one magnitude be greater than the same multiple of another then the former magnitude is greater than the latter ...
Page 2
... greater or less according as the difference of direction of its arms is greater or less .. It is evident that Two straight lines - cannot enclose a space . Hence it follows that Two straight lines cannot have a common segment .. A. B H ...
... greater or less according as the difference of direction of its arms is greater or less .. It is evident that Two straight lines - cannot enclose a space . Hence it follows that Two straight lines cannot have a common segment .. A. B H ...
Page 22
... greater than either of the interior and opposite angles . B Let the side BC of △ ABC be produced to D. Then shall the ACD be > either of the S BAC , ABC . Bisect AC in E ; join BE and produce BE to F , making EF BE . H Join CF. Then ...
... greater than either of the interior and opposite angles . B Let the side BC of △ ABC be produced to D. Then shall the ACD be > either of the S BAC , ABC . Bisect AC in E ; join BE and produce BE to F , making EF BE . H Join CF. Then ...
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Common terms and phrases
Algebra Arithmetic base BEGINNERS Cambridge centre chord Christ's College circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle John's College Latin Let ABC line bisecting locus magnitudes Mathematical meet Owens College parallel parallelogram perimeter perpendicular plane PROBLEM produced Professor proportional PROPOSITION radius ratio rect rectangle rectangle contained rectilineal figure regular polygon render respectively revised rhombus right angles Schools Second Edition segment Similarly squares on AC straight line joining student tangent THEOREM TRIGONOMETRY twice rectangle twice the squares Uppingham School vertex
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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 15 - ... and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bo.iits of the Solar System, and of a few stars, omitting all minutiit of Elementary Class- Books — continued. formulcE, and all troublesome details of calculation.