... parallel to the base ABCD ; thus the parallelopiped AG will be divided into p solids , which will also be parallelopipeds having equal bases ( 7. ) and equal altitudes , there- fore they will be equal among themselves ; and in like ...

... parallel Planes , AOI and RGE , they are equal Parallelopipeds ; which is evident , from the foregoing ; each being equal to PFHN . CASE III . When the Parallelopipeds have no Face common nor fimilar Figures . Let the Parallelopipeds ...

... parallel to the base ABCD ; thus the parallelopiped AG will be divided into p folids , which will alfo be parallelopipeds having equal bafes ( 7. ) and equal altitudes , there- fore they will be equal among themfelves ; and in like ...

Benjamin Peirce. Ratio of right Parallelopipeds . 357. Theorem . Two right parallelopipeds are to each other as the products of their bases by their al- titudes . Proof . Let the two right parallelopipeds be ABCD EFGH , AKLM NOPQ ...

... parallelopiped AG will be to the parallelopiped AL as the number m to the number n , that is , as AE the altitude of the former to Al the altitude of the latter . THEOREM IX . - Two rectangular parallelopipeds AG , AK , which have the ...

... parallelopipeds upon them are together greater than EK : and EK is equal to the e A. 5 . cylinder ABCD ; therefore the parallelopipeds upon the rect- angles are greater than the cylinder ; and they are also less , be- cause they are ...

... parallelopipeds upon them are together greater than EK : and EK is equal to the c A. 5 . cylinder ABCD ; therefore the parallelopipeds upon the rect- angles are greater than the cylinder ; and they are alfo lefs , be- cause they are ...

... parallelopiped will be equivalent to the parallelopiped AG ( 4 ) ; for the same rea- son the third parallelopiped will be equivalent to the paral- lelopiped AL therefore the two parallelopipeds AG , AL , which have the same base and the ...

... parallelopipeds Y and Z on these bases . Then , if the upright parallelopipeds AF and GO be constituted on the bases AC and GK , with the altitudes AE and GM , they will be equal to the parallelopipeds Y and Z ( 7. 3. Sup . ) . Now ...

... Parallelopipeds upon the same base , and between the same parallel planes , are equal to one another . Let ABCD be the common base of two parallelopipeds , which have their opposite bases EFGH and KLMN lying in the same plane : the two ...