Cavalieri's Principle/Extension
Contents
Theorem
Let two solid figures $S_1$ and $S_2$ have equal height.
Let the areas of the sections made by planes parallel to their bases and at equal distances from the bases always have the same ratio.
Then the volumes of $S_1$ and $S_2$ are in that same ratio.
Proof
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
Source of Name
This entry was named for Bonaventura Cavalieri.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.14$: Cavalieri ($1598$ – $1647$)
